SHSAT Math Quiz: Multi Step Equations
20 questions · exam conditions
0:00
Multi Step EquationsQuestion 1 of 20

Solve: 9−2(3−4x)=1.9-2(3-4x)=1.

−14-\dfrac14
14\dfrac14
−12-\dfrac12
12\dfrac12
← Back to quizzes

SHSAT Math Quiz

SHSAT Math Quiz: Multi Step Equations

Practice Multi Step Equations in SHSAT Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Multi Step Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Solve: 9−2(3−4x)=1.9-2(3-4x)=1.

  1. −14-\dfrac14 (correct answer)
  2. 14\dfrac14
  3. −12-\dfrac12
  4. 12\dfrac12
Explanation: This is a linear equation that requires you to use the distributive property and inverse operations to isolate the variable. When you see parentheses with a coefficient in front, always distribute first before combining like terms. Start by distributing the −2-2 to both terms inside the parentheses: 9−2(3−4x)=9−6+8x=3+8x9 - 2(3 - 4x) = 9 - 6 + 8x = 3 + 8x. So your equation becomes 3+8x=13 + 8x = 1. Next, subtract 3 from both sides: 8x=−28x = -2. Finally, divide both sides by 8: x=−28=−14x = -\frac{2}{8} = -\frac{1}{4}. Choice A gives −14-\frac{1}{4}, which matches our solution. Choice B gives 14\frac{1}{4}, which you'd get if you made a sign error when distributing the negative or when solving 8x=−28x = -2. Choice C gives −12-\frac{1}{2}, which results from forgetting to distribute the −2-2 to the 4x4x term, leaving you with 9−6−4x=19 - 6 - 4x = 1, so 3−4x=13 - 4x = 1 and x=12x = \frac{1}{2}, then incorrectly applying a negative sign. Choice D gives 12\frac{1}{2}, which comes from the same distribution error but without the final sign mistake. The key strategy here is to work methodically: distribute first, combine like terms, then use inverse operations. Double-check your distribution step since that's where most errors occur—make sure you apply the outside coefficient to every term inside the parentheses, keeping track of signs carefully.

Question 2

Solve for xx: −3(4x+5)+2=−10.-3(4x+5)+2=-10.

  1. −14-\dfrac14 (correct answer)
  2. 14\dfrac14
  3. −34-\dfrac34
  4. 34\dfrac34
Explanation: When you encounter a linear equation with parentheses and multiple terms, your goal is to systematically isolate the variable using inverse operations in the proper order. Start by distributing the −3-3 across the parentheses: −3(4x+5)=−12x−15-3(4x+5) = -12x - 15. This gives you −12x−15+2=−10-12x - 15 + 2 = -10. Combine like terms on the left: −12x−13=−10-12x - 13 = -10. Add 13 to both sides: −12x=−10+13=3-12x = -10 + 13 = 3. Finally, divide both sides by −12-12: x=3−12=−14x = \frac{3}{-12} = -\frac{1}{4}. Let's verify: −3(4(−14)+5)+2=−3(−1+5)+2=−3(4)+2=−12+2=−10-3(4(-\frac{1}{4})+5)+2 = -3(-1+5)+2 = -3(4)+2 = -12+2 = -10 ✓ Looking at the wrong answers: Choice B gives 14\frac{1}{4}, which you'd get if you forgot the negative sign when dividing by −12-12. Choice C gives −34-\frac{3}{4}, which results from incorrectly distributing or combining like terms—perhaps getting −4x=3-4x = 3 instead of −12x=3-12x = 3. Choice D gives 34\frac{3}{4}, combining the sign error from choice B with the coefficient error from choice C. The correct answer is A: −14-\frac{1}{4}. Strategy tip: Always distribute carefully and track your negative signs. After solving, substitute your answer back into the original equation to catch arithmetic mistakes—this verification step is especially valuable on timed exams when you might rush through calculations.

Question 3

Solve: 4x−7(2−x)=45.4x-7(2-x)=45.

  1. 5911\dfrac{59}{11} (correct answer)
  2. 4511\dfrac{45}{11}
  3. 4111\dfrac{41}{11}
  4. 6311\dfrac{63}{11}
Explanation: This is a linear equation that requires you to distribute, combine like terms, and isolate the variable. When you see an equation with parentheses, your first step should always be to distribute to eliminate them. Start by distributing the −7-7 to both terms inside the parentheses: 4x−7(2)−7(−x)=454x - 7(2) - 7(-x) = 45, which gives you 4x−14+7x=454x - 14 + 7x = 45. Now combine like terms on the left side: 11x−14=4511x - 14 = 45. Add 14 to both sides: 11x=5911x = 59. Finally, divide both sides by 11: x=5911x = \frac{59}{11}. Looking at the wrong answers, choice B (4511\frac{45}{11}) likely comes from forgetting to add 14 to the right side after getting 11x−14=4511x - 14 = 45, incorrectly concluding that 11x=4511x = 45. Choice C (4111\frac{41}{11}) probably results from a sign error when distributing—if you mistakenly got 4x−14−7x=454x - 14 - 7x = 45, you'd have −3x−14=45-3x - 14 = 45, leading to −3x=59-3x = 59 and x=−593x = -\frac{59}{3}, though this doesn't match exactly. Choice D (6311\frac{63}{11}) might come from an arithmetic error when combining like terms or solving. Remember: distribution problems on the SHSAT often include negative signs that can trip you up. Always be extra careful with signs when distributing, and double-check your work by substituting your answer back into the original equation to verify it's correct.

Question 4

Solve: −0.5(6x−8)+4=7.-0.5(6x-8)+4=7.

  1. 13\dfrac13 (correct answer)
  2. 23\dfrac23
  3. −13-\dfrac13
  4. −23-\dfrac23
Explanation: This is a linear equation with decimals and parentheses that requires careful order of operations and algebraic manipulation. When you encounter equations like this, work systematically through distribution, combining like terms, and isolating the variable. Start by distributing the −0.5-0.5 to both terms inside the parentheses: −0.5(6x)+(−0.5)(−8)+4=7-0.5(6x) + (-0.5)(-8) + 4 = 7, which gives you −3x+4+4=7-3x + 4 + 4 = 7. Combining like terms on the left side: −3x+8=7-3x + 8 = 7. Subtract 8 from both sides: −3x=−1-3x = -1. Finally, divide both sides by −3-3: x=−1−3=13x = \frac{-1}{-3} = \frac{1}{3}. This matches choice A. Let's examine why the other answers are incorrect. Choice B (23\frac{2}{3}) likely results from an error in the final division step, perhaps incorrectly calculating −1−3\frac{-1}{-3} or making an arithmetic mistake earlier. Choice C (−13-\frac{1}{3}) comes from forgetting that dividing two negative numbers gives a positive result—this is what you'd get if you calculated −1−3=−13\frac{-1}{-3} = -\frac{1}{3}. Choice D (−23-\frac{2}{3}) combines both errors: incorrect signs and wrong numerator. You can verify: substituting x=13x = \frac{1}{3} back into the original equation gives −0.5(6⋅13−8)+4=−0.5(2−8)+4=−0.5(−6)+4=3+4=7-0.5(6 \cdot \frac{1}{3} - 8) + 4 = -0.5(2-8) + 4 = -0.5(-6) + 4 = 3 + 4 = 7 ✓ Strategy tip: Always distribute carefully with decimals, and remember that dividing two negative numbers yields a positive result. Check your answer by substituting back into the original equation.

Question 5

Solve: 5x−24+3=8.\dfrac{5x-2}{4}+3=8.

  1. 225\dfrac{22}{5} (correct answer)
  2. 112\dfrac{11}{2}
  3. 245\dfrac{24}{5}
  4. 235\dfrac{23}{5}
Explanation: When you encounter a linear equation with fractions, your goal is to isolate the variable by systematically undoing the operations in reverse order. Starting with 5x−24+3=8\dfrac{5x-2}{4}+3=8, first eliminate the constant term by subtracting 3 from both sides: 5x−24=5\dfrac{5x-2}{4}=5. Next, clear the fraction by multiplying both sides by 4: 5x−2=205x-2=20. Add 2 to both sides: 5x=225x=22. Finally, divide by 5: x=225x=\dfrac{22}{5}. Let's examine why each answer choice might appear. Choice A, 225\dfrac{22}{5}, is correct as shown above. Choice B, 112\dfrac{11}{2}, likely results from making an error when clearing the fraction—perhaps multiplying only the numerator by 4 instead of the entire left side, leading to 5x−2=205x-2=20 becoming 20x−2=2020x-2=20, then x=2220=1110x=\dfrac{22}{20}=\dfrac{11}{10}, or from other algebraic mistakes. Choice C, 245\dfrac{24}{5}, might come from incorrectly handling the subtraction step, perhaps adding 2 instead of subtracting when isolating 5x5x. Choice D, 235\dfrac{23}{5}, could result from arithmetic errors in the final steps or confusion about order of operations. The key strategy here is working systematically: handle addition/subtraction before multiplication/division, and always perform the same operation to both sides. When dealing with fractions in equations, multiply both sides by the denominator to clear them early—this prevents mistakes and simplifies your work.

Question 6

Solve for xx: 5(2x−3)−7=18.5(2x-3)-7=18.

  1. 4 (correct answer)
  2. 5
  3. 3
  4. 2
Explanation: When you encounter a linear equation with parentheses like this one, your goal is to systematically isolate the variable using the order of operations in reverse. This tests your ability to work with multi-step equations involving the distributive property. Start by applying the distributive property to expand 5(2x−3)5(2x-3): 5⋅2x−5⋅3=10x−155 \cdot 2x - 5 \cdot 3 = 10x - 15. The equation becomes 10x−15−7=1810x - 15 - 7 = 18. Combine like terms: 10x−22=1810x - 22 = 18. Add 22 to both sides: 10x=4010x = 40. Finally, divide both sides by 10: x=4x = 4. Let's verify: 5(2⋅4−3)−7=5(8−3)−7=5(5)−7=25−7=185(2 \cdot 4 - 3) - 7 = 5(8 - 3) - 7 = 5(5) - 7 = 25 - 7 = 18 ✓ Choice B (5) likely comes from the intermediate step where you get 2x−3=52x - 3 = 5 if you incorrectly divide by 5 too early, then solve 2x=82x = 8 to get x=4x = 4, but mistakenly write down the 5. Choice C (3) results from solving 2x−3=52x - 3 = 5 and getting 2x=82x = 8, then making an arithmetic error. Choice D (2) occurs if you make multiple errors—perhaps incorrectly distributing or combining terms, leading to x=2x = 2. The key strategy here is to work step-by-step without skipping ahead. Always distribute first, combine like terms, then use inverse operations to isolate the variable. Double-check your answer by substituting back into the original equation—this catches most computational errors and confirms your solution.

Question 7

Marcus is solving the equation 3(2x−5)+4x=2x+73(2x - 5) + 4x = 2x + 7. After distributing and combining like terms on the left side, he gets 8x−15=2x+78x - 15 = 2x + 7. What value of xx satisfies the original equation?

  1. x=113x = \frac{11}{3} (correct answer)
  2. x=226x = \frac{22}{6}
  3. x=83x = \frac{8}{3}
  4. x=41x = \frac{4}{1}
Explanation: Starting from Marcus's work: 8x−15=2x+78x - 15 = 2x + 7. Subtract 2x2x from both sides: 6x−15=76x - 15 = 7. Add 15 to both sides: 6x=226x = 22. Divide by 6: x=226=113x = \frac{22}{6} = \frac{11}{3}. Choice B shows the unreduced fraction 226\frac{22}{6}, which equals 113\frac{11}{3} but isn't in simplest form. Choice C results from incorrectly getting 6x=166x = 16 instead of 6x=226x = 22. Choice D comes from the error 6x=246x = 24.

Question 8

Solve for xx: 7x3+5=20.\dfrac{7x}{3}+5=20.

  1. 457\dfrac{45}{7} (correct answer)
  2. 66
  3. 157\dfrac{15}{7}
  4. 203\dfrac{20}{3}
Explanation: When you encounter a linear equation with fractions, your goal is to isolate the variable by using inverse operations in the correct order. Starting with 7x3+5=20\frac{7x}{3} + 5 = 20, first subtract 5 from both sides to eliminate the constant term: 7x3=15\frac{7x}{3} = 15. Next, multiply both sides by 3 to clear the fraction: 7x=457x = 45. Finally, divide both sides by 7 to solve for x: x=457x = \frac{45}{7}. Let's examine why each answer choice is right or wrong. Choice A, 457\frac{45}{7}, is correct as we just demonstrated. Choice B, 6, likely comes from incorrectly treating the equation as 7x+5=207x + 5 = 20 (ignoring the denominator 3), which would give x=157×73=5x = \frac{15}{7} \times \frac{7}{3} = 5, but that's still not 6—this suggests multiple computational errors. Choice C, 157\frac{15}{7}, results from forgetting to divide by 7 in the final step; students who get this stopped at 7x=157x = 15 instead of 7x=457x = 45. Choice D, 203\frac{20}{3}, appears to come from mishandling the fraction entirely, perhaps trying to cross-multiply incorrectly. Always verify your solution by substituting back into the original equation. With x=457x = \frac{45}{7}: 7⋅4573+5=453+5=15+5=20\frac{7 \cdot \frac{45}{7}}{3} + 5 = \frac{45}{3} + 5 = 15 + 5 = 20 ✓. On the SHSAT, fraction problems often include answer choices that represent common algebraic mistakes—double-check your arithmetic at each step.

Question 9

Solve: 6[2−(x−3)]=24.6\bigl[2-(x-3)\bigr]=24.

  1. 1 (correct answer)
  2. 3
  3. 2
  4. 4
Explanation: This question tests your ability to solve linear equations with nested grouping symbols. When you encounter brackets and parentheses together, work from the inside out and follow the order of operations carefully. Start by dividing both sides by 6 to simplify: 2−(x−3)=42-(x-3) = 4 Next, distribute the negative sign to remove the parentheses. Remember that the minus sign in front of (x−3)(x-3) affects both terms inside: 2−x+3=42-x+3 = 4 Combine like terms on the left side: 5−x=45-x = 4 Subtract 5 from both sides: −x=−1-x = -1 Finally, multiply both sides by -1: x=1x = 1 You can verify this by substituting back into the original equation: 6[2−(1−3)]=6[2−(−2)]=6[2+2]=6(4)=246[2-(1-3)] = 6[2-(-2)] = 6[2+2] = 6(4) = 24 ✓ Looking at the wrong answers: Choice B (3) comes from incorrectly handling the nested grouping symbols, likely by not properly distributing the negative sign. Choice C (2) might result from arithmetic errors when combining like terms or solving the final step. Choice D (4) could come from incorrectly simplifying 2−(x−3)2-(x-3) or making sign errors throughout the process. When solving equations with multiple grouping symbols, always work systematically from the innermost parentheses outward. Double-check your distribution of negative signs, as this is where most errors occur. Always verify your answer by substituting back into the original equation.

Question 10

Solve: −2[3−5(x−2)]=28.-2\bigl[3-5(x-2)\bigr]=28.

  1. 275\dfrac{27}{5} (correct answer)
  2. 145\dfrac{14}{5}
  3. 112\dfrac{11}{2}
  4. 55
Explanation: This is a multi-step linear equation that requires careful attention to the order of operations and algebraic manipulation. When you see nested brackets with multiple operations, work systematically from the inside out. Start by expanding the expression inside the brackets. First, distribute the −5-5 to both terms in (x−2)(x-2): −5(x−2)=−5x+10-5(x-2) = -5x + 10. Now the expression becomes 3−(−5x+10)=3+5x−10=5x−73 - (-5x + 10) = 3 + 5x - 10 = 5x - 7. So your equation is now −2(5x−7)=28-2(5x - 7) = 28. Distribute the −2-2: −10x+14=28-10x + 14 = 28. Subtract 1414 from both sides: −10x=14-10x = 14. Finally, divide by −10-10: x=−1410=−75x = -\frac{14}{10} = -\frac{7}{5}. Wait—this doesn't match any answer choice! Let me recalculate more carefully. From 3−5(x−2)3 - 5(x-2): the −5-5 distributes to get 3−5x+10=13−5x3 - 5x + 10 = 13 - 5x. Now −2(13−5x)=28-2(13 - 5x) = 28 becomes −26+10x=28-26 + 10x = 28. Adding 2626 to both sides: 10x=5410x = 54, so x=5410=275x = \frac{54}{10} = \frac{27}{5}. Choice A (275\frac{27}{5}) is correct. Choice B (145\frac{14}{5}) likely comes from forgetting to distribute the −2-2 to the constant term. Choice C (112\frac{11}{2}) might result from sign errors when distributing. Choice D (55) could come from calculation mistakes or improper fraction reduction. Remember: when solving equations with nested operations, distribute step-by-step and track your signs carefully. Double-check by substituting your answer back into the original equation.

Question 11

Solve: 0.75x+1.5(4−x)=6.0.75x+1.5(4-x)=6.

  1. 0 (correct answer)
  2. 2
  3. 4
  4. 6
Explanation: When you encounter a linear equation with decimals and parentheses, your goal is to simplify systematically using the distributive property and combining like terms. Start by distributing the 1.5 to both terms inside the parentheses: 0.75x+1.5(4)+1.5(−x)=60.75x + 1.5(4) + 1.5(-x) = 6, which becomes 0.75x+6−1.5x=60.75x + 6 - 1.5x = 6. Next, combine the like terms on the left side. The x-terms are 0.75x−1.5x=−0.75x0.75x - 1.5x = -0.75x, so you have −0.75x+6=6-0.75x + 6 = 6. Subtract 6 from both sides: −0.75x=0-0.75x = 0. Dividing both sides by -0.75 gives you x=0x = 0. Let's verify: substituting x=0x = 0 into the original equation gives 0.75(0)+1.5(4−0)=0+1.5(4)=60.75(0) + 1.5(4-0) = 0 + 1.5(4) = 6. ✓ Looking at the wrong answers: Choice B (x=2x = 2) would give 0.75(2)+1.5(2)=1.5+3=4.5≠60.75(2) + 1.5(2) = 1.5 + 3 = 4.5 \neq 6. Choice C (x=4x = 4) would yield 0.75(4)+1.5(0)=3≠60.75(4) + 1.5(0) = 3 \neq 6. Choice D (x=6x = 6) produces 0.75(6)+1.5(−2)=4.5−3=1.5≠60.75(6) + 1.5(-2) = 4.5 - 3 = 1.5 \neq 6. These wrong answers likely come from calculation errors in distributing or combining like terms. Study tip: When working with decimal coefficients, consider converting to fractions (0.75 = 3/4, 1.5 = 3/2) if that feels more comfortable, or always double-check your arithmetic when combining decimal terms.

Question 12

Solve: 23(9−6x)=4.\dfrac23(9-6x)=4.

  1. 12\dfrac12 (correct answer)
  2. 11
  3. 13\dfrac13
  4. 23\dfrac23
Explanation: This is a linear equation that requires you to isolate the variable through systematic algebraic steps. When you see fractions multiplied by expressions in parentheses, your goal is to clear the fraction first, then work with the resulting simpler equation. Start by multiplying both sides by 32\frac{3}{2} (the reciprocal of 23\frac{2}{3}) to eliminate the fraction: 9−6x=4⋅32=69 - 6x = 4 \cdot \frac{3}{2} = 6. Now you have the simpler equation 9−6x=69 - 6x = 6. Subtract 9 from both sides: −6x=−3-6x = -3. Finally, divide both sides by -6: x=−3−6=12x = \frac{-3}{-6} = \frac{1}{2}. This confirms that A) 12\frac{1}{2} is correct. Let's examine why the other answers are wrong. Choice B) 11 likely comes from making an error when clearing the fraction or solving −6x=−3-6x = -3—perhaps dividing by -3 instead of -6. Choice C) 13\frac{1}{3} might result from incorrectly handling the fraction multiplication or making a sign error during the solving process. Choice D) 23\frac{2}{3} could come from confusing this value with the original coefficient in the problem, or from computational mistakes when working with the fractions. To verify your answer, always substitute back into the original equation: 23(9−6⋅12)=23(9−3)=23(6)=4\frac{2}{3}(9 - 6 \cdot \frac{1}{2}) = \frac{2}{3}(9 - 3) = \frac{2}{3}(6) = 4 ✓ Strategy tip: When solving equations with fractions, eliminate the fraction first by multiplying by its reciprocal. This makes the algebra much cleaner and reduces calculation errors.

Question 13

Solve: 7(x−2)−3(x+4)+9=0.7(x-2)-3(x+4)+9=0.

  1. 174\dfrac{17}{4} (correct answer)
  2. 194\dfrac{19}{4}
  3. 44
  4. 154\dfrac{15}{4}
Explanation: When you encounter a linear equation with parentheses and multiple terms like this one, your goal is to systematically simplify by distributing, combining like terms, and isolating the variable. Start by distributing each coefficient to the terms inside the parentheses: 7(x−2)=7x−147(x-2) = 7x - 14 and −3(x+4)=−3x−12-3(x+4) = -3x - 12. This gives you: 7x−14−3x−12+9=07x - 14 - 3x - 12 + 9 = 0. Next, combine like terms. The xx terms: 7x−3x=4x7x - 3x = 4x. The constants: −14−12+9=−17-14 - 12 + 9 = -17. Your equation becomes: 4x−17=04x - 17 = 0. Finally, solve for xx by adding 17 to both sides: 4x=174x = 17, so x=174x = \frac{17}{4}. Let's examine why the other answers are wrong. Choice B (194\frac{19}{4}) likely results from an error in combining constants—perhaps calculating −14−12+9=−15-14 - 12 + 9 = -15 instead of −17-17. Choice C (44) might come from forgetting to distribute properly or from confusing the coefficient of xx with the final answer. Choice D (154\frac{15}{4}) could result from sign errors during distribution, such as treating −3(x+4)-3(x+4) as −3x+12-3x + 12 instead of −3x−12-3x - 12. The correct answer is A: 174\frac{17}{4}. Study tip: Always work step-by-step with distribution problems: distribute first, then combine like terms, then isolate the variable. Double-check your arithmetic at each step, especially with negative signs—they're the most common source of errors in these problems.

Question 14

Solve: 25(15−10x)+7=−1.\dfrac25(15-10x)+7=-1.

  1. 3.5 (correct answer)
  2. 2.5
  3. 4
  4. 3
Explanation: When solving linear equations with fractions and parentheses, work systematically through the order of operations while isolating the variable step by step. Start by distributing the fraction 25\frac{2}{5} to both terms inside the parentheses: 25(15−10x)=25⋅15−25⋅10x=6−4x\frac{2}{5}(15-10x) = \frac{2}{5} \cdot 15 - \frac{2}{5} \cdot 10x = 6 - 4x The equation becomes: 6−4x+7=−16 - 4x + 7 = -1 Combine like terms on the left side: 13−4x=−113 - 4x = -1 Subtract 13 from both sides: −4x=−14-4x = -14 Divide both sides by -4: x=144=3.5x = \frac{14}{4} = 3.5 Choice A (3.5) is correct. Choice B (2.5) likely results from an error when combining constants—perhaps calculating 6+7=116 + 7 = 11 instead of 13, leading to −4x=−12-4x = -12 and x=3x = 3. Wait, that would give 3, not 2.5. Choice B probably comes from a sign error or incorrect distribution. Choice D (3) occurs when you make an arithmetic mistake with the constants, getting −4x=−12-4x = -12. Choice C (4) might result from incorrectly distributing the fraction or making a sign error during isolation. You can verify: 25(15−10(3.5))+7=25(15−35)+7=25(−20)+7=−8+7=−1\frac{2}{5}(15-10(3.5))+7 = \frac{2}{5}(15-35)+7 = \frac{2}{5}(-20)+7 = -8+7 = -1 ✓ Strategy tip: Always distribute fractions carefully to each term in parentheses, and verify your answer by substituting back into the original equation. This catches arithmetic errors that commonly appear in SHSAT problems.

Question 15

Solve: 11−x3=8.11-\dfrac{x}{3}=8.

  1. 9 (correct answer)
  2. 6
  3. 3
  4. 12
Explanation: This is a one-step linear equation that requires isolating the variable xx. When you see an equation with a fraction involving the variable, your goal is to eliminate the fraction by using inverse operations. Starting with 11−x3=811-\dfrac{x}{3}=8, first isolate the fraction term by subtracting 11 from both sides: −x3=8−11=−7-\dfrac{x}{3} = 8-11 = -7. Now you have −x3=−7-\dfrac{x}{3} = -7. To solve for xx, multiply both sides by −3-3: x=(−7)×(−3)=21x = (-7) \times (-3) = 21. Wait—21 isn't among the choices, so let me check this calculation. Actually, let's verify by substituting our potential answers back into the original equation. For choice A) x=9x = 9: 11−93=11−3=811-\dfrac{9}{3} = 11-3 = 8 ✓ For choice B) x=6x = 6: 11−63=11−2=9≠811-\dfrac{6}{3} = 11-2 = 9 \neq 8 For choice C) x=3x = 3: 11−33=11−1=10≠811-\dfrac{3}{3} = 11-1 = 10 \neq 8 For choice D) x=12x = 12: 11−123=11−4=7≠811-\dfrac{12}{3} = 11-4 = 7 \neq 8 The answer is A) 9. Going back to my algebra: from −x3=−7-\dfrac{x}{3} = -7, I should multiply both sides by −3-3 to get x=21x = 21... but that's not matching. Let me recalculate: 11−8=311-8=3, so x3=3\dfrac{x}{3}=3, which means x=9x=9. Choices B, C, and D all produce different values when substituted back into the original equation, showing they're incorrect solutions. Strategy tip: Always verify your answer by substituting back into the original equation—this catches arithmetic errors and confirms your solution works.

Question 16

Solve: 32[4−(2x−3)]=9.\dfrac32\bigl[4-(2x-3)\bigr]=9.

  1. 12\dfrac12 (correct answer)
  2. 11
  3. 34\dfrac34
  4. 14\dfrac14
Explanation: This question tests your ability to solve linear equations with fractions and nested operations. When you see an equation like this, work systematically from the outside in, following the order of operations in reverse. Start by isolating the bracketed expression. Divide both sides by 32\frac{3}{2}, which is the same as multiplying by 23\frac{2}{3}: 4−(2x−3)=9⋅23=64-(2x-3) = 9 \cdot \frac{2}{3} = 6 Next, simplify the left side by distributing the negative sign: 4−2x+3=64-2x+3 = 6 7−2x=67-2x = 6 Subtract 7 from both sides: −2x=−1-2x = -1 Divide by -2: x=12x = \frac{1}{2} Let's verify: 32[4−(2⋅12−3)]=32[4−(1−3)]=32[4−(−2)]=32[6]=9\frac{3}{2}[4-(2 \cdot \frac{1}{2}-3)] = \frac{3}{2}[4-(1-3)] = \frac{3}{2}[4-(-2)] = \frac{3}{2}[6] = 9 ✓ The correct answer is A) 12\frac{1}{2}. Choice B) 1 would result from incorrectly solving −2x=−2-2x = -2 instead of −2x=−1-2x = -1. Choice C) 34\frac{3}{4} might come from arithmetic errors when working with the fractions. Choice D) 14\frac{1}{4} could result from incorrectly dividing by 4 instead of -2 in the final step. Study tip: When solving equations with fractions, eliminate the fraction first by multiplying both sides by its reciprocal. Always verify your answer by substituting back into the original equation—this catches arithmetic mistakes and ensures you didn't miss a step in the algebraic manipulation.

Question 17

Solve for xx: 2(x−3)+4(x+1)=10.2(x-3)+4(x+1)=10.

  1. 2 (correct answer)
  2. 1
  3. 3
  4. 4
Explanation: When you encounter a linear equation with parentheses and multiple terms, your goal is to systematically simplify and isolate the variable. This tests your ability to apply the distributive property and combine like terms. Let's solve 2(x−3)+4(x+1)=102(x-3)+4(x+1)=10 step by step. First, distribute each coefficient: 2(x−3)2(x-3) becomes 2x−62x-6, and 4(x+1)4(x+1) becomes 4x+44x+4. The equation is now 2x−6+4x+4=102x-6+4x+4=10. Next, combine like terms on the left side: 2x+4x=6x2x+4x=6x and −6+4=−2-6+4=-2, giving you 6x−2=106x-2=10. Add 2 to both sides: 6x=126x=12. Finally, divide both sides by 6: x=2x=2. Let's verify: 2(2−3)+4(2+1)=2(−1)+4(3)=−2+12=102(2-3)+4(2+1)=2(-1)+4(3)=-2+12=10 ✓ Looking at the wrong answers: Choice B (x=1x=1) gives you 2(−2)+4(2)=4≠102(-2)+4(2)=4 \neq 10. Choice C (x=3x=3) yields 2(0)+4(4)=16≠102(0)+4(4)=16 \neq 10. Choice D (x=4x=4) results in 2(1)+4(5)=22≠102(1)+4(5)=22 \neq 10. These incorrect values likely come from arithmetic errors during distribution or combining like terms. The correct answer is A. Strategy tip: Always verify your solution by substituting back into the original equation. This catches calculation mistakes and confirms your answer, especially important on standardized tests where small errors lead to wrong answer choices that seem plausible.

Question 18

Solve: 4x−13−29=5.\dfrac{4x-1}{3}-\dfrac{2}{9}=5.

  1. 256\dfrac{25}{6} (correct answer)
  2. 509\dfrac{50}{9}
  3. 236\dfrac{23}{6}
  4. 112\dfrac{11}{2}
Explanation: When you encounter an equation with fractions, your goal is to isolate the variable by systematically eliminating the fractions and simplifying. This question tests your ability to work with linear equations containing fractions. Start by getting all terms with fractions on one side. Add 29\frac{2}{9} to both sides: 4x−13=5+29\frac{4x-1}{3} = 5 + \frac{2}{9} To add 5+295 + \frac{2}{9}, convert 5 to ninths: 5=4595 = \frac{45}{9}. So: 4x−13=459+29=479\frac{4x-1}{3} = \frac{45}{9} + \frac{2}{9} = \frac{47}{9} Now multiply both sides by 3 to eliminate the remaining fraction: 4x−1=3⋅479=1419=4734x - 1 = 3 \cdot \frac{47}{9} = \frac{141}{9} = \frac{47}{3} Add 1 to both sides: 4x=473+1=473+33=5034x = \frac{47}{3} + 1 = \frac{47}{3} + \frac{3}{3} = \frac{50}{3} Finally, divide by 4: x=503÷4=503⋅14=5012=256x = \frac{50}{3} \div 4 = \frac{50}{3} \cdot \frac{1}{4} = \frac{50}{12} = \frac{25}{6} This confirms answer A) 256\frac{25}{6}. Answer B) 509\frac{50}{9} likely results from incorrectly adding fractions in the early steps. Answer C) 236\frac{23}{6} suggests an arithmetic error when combining 473+1\frac{47}{3} + 1. Answer D) 112\frac{11}{2} might come from mishandling the fraction operations or making errors in the final division step. Strategy tip: Always work systematically with fraction equations: clear fractions step by step, convert whole numbers to fractions with common denominators, and double-check your arithmetic at each stage.

Question 19

Solve: 6−2[4−3(x−2)]=−18.6-2\bigl[4-3(x-2)\bigr]=-18.

  1. −23-\dfrac23 (correct answer)
  2. −1-1
  3. 23\dfrac23
  4. 11
Explanation: When you encounter a multi-step equation with nested brackets like this, your success depends on working systematically from the inside out, following the order of operations. Start with the innermost parentheses: 3(x−2)=3x−63(x-2) = 3x - 6. Now substitute this back: 6−2[4−(3x−6)]=−186 - 2[4 - (3x - 6)] = -18. Simplify inside the brackets: 4−(3x−6)=4−3x+6=10−3x4 - (3x - 6) = 4 - 3x + 6 = 10 - 3x. The equation becomes: 6−2(10−3x)=−186 - 2(10 - 3x) = -18. Distribute the −2-2: 6−20+6x=−186 - 20 + 6x = -18, which simplifies to −14+6x=−18-14 + 6x = -18. Add 14 to both sides: 6x=−46x = -4. Therefore: x=−46=−23x = -\frac{4}{6} = -\frac{2}{3}. Looking at the wrong answers: Choice B (−1-1) likely comes from making an error when distributing the negative sign or combining like terms. Choice C (23\frac{2}{3}) is the positive version of the correct answer—a common mistake when students lose track of negative signs during the multi-step process. Choice D (11) might result from computational errors in the final division step or earlier sign errors. The correct answer is A: −23-\frac{2}{3}. Strategy tip: With nested grouping symbols, always work from the innermost outward and double-check your sign changes at each step. Many SHSAT algebra errors happen when students rush through the distribution of negative signs—slow down and verify each transformation.

Question 20

Solve: 10−4(1−x5)=6.10-4\Bigl(1-\dfrac{x}{5}\Bigr)=6.

  1. 0 (correct answer)
  2. 5
  3. 2
  4. 4
Explanation: When you encounter a linear equation with fractions and parentheses like this one, your goal is to systematically isolate the variable by working through the order of operations in reverse. Start by simplifying the left side. First, distribute the −4-4 through the parentheses: 10−4(1−x5)=10−4+4x5=6+4x510 - 4(1 - \frac{x}{5}) = 10 - 4 + \frac{4x}{5} = 6 + \frac{4x}{5}. Now your equation becomes 6+4x5=66 + \frac{4x}{5} = 6. Subtract 6 from both sides: 4x5=0\frac{4x}{5} = 0. To solve for xx, multiply both sides by 54\frac{5}{4}: x=0⋅54=0x = 0 \cdot \frac{5}{4} = 0. You can verify this by substituting back: 10−4(1−05)=10−4(1)=610 - 4(1 - \frac{0}{5}) = 10 - 4(1) = 6 ✓ Choice A (0) is correct. Choice B (5) likely comes from incorrectly thinking that 4x5=0\frac{4x}{5} = 0 means x=5x = 5, possibly from confusing the denominator with the solution. Choice C (2) might result from arithmetic errors when distributing or combining terms. Choice D (4) could come from mistakenly thinking the coefficient 4 in 4x5\frac{4x}{5} becomes the answer, or from errors in the distribution step. Remember that when you have axb=0\frac{ax}{b} = 0 where a≠0a \neq 0 and b≠0b \neq 0, the solution is always x=0x = 0. Any non-zero number multiplied by zero equals zero, regardless of what fraction it's part of. This pattern appears frequently on the SHSAT, so recognizing it quickly will save you time.