ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: One Variable Linear Equations
20 questions · exam conditions
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One Variable Linear EquationsQuestion 1 of 20

Which of the following is the solution to the equation 3(x+2)=5x−43(x + 2) = 5x - 4?

x=−1x = -1
x=1x = 1
x=3x = 3
x=5x = 5
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ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: One Variable Linear Equations

Practice One Variable Linear Equations in ACCUPLACER Quantitative Reasoning, Algebra & Statistics 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 One Variable Linear Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Quantitative Reasoning, Algebra & Statistics.

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

Which of the following is the solution to the equation 3(x+2)=5x−43(x + 2) = 5x - 4?

  1. x=−1x = -1
  2. x=1x = 1
  3. x=3x = 3
  4. x=5x = 5 (correct answer)
Explanation: To solve the equation, first distribute the 3 on the left side: 3x+6=5x−43x + 6 = 5x - 4. Next, gather the variable terms on one side and the constant terms on the other. Subtract 3x3x from both sides to get 6=2x−46 = 2x - 4. Then, add 4 to both sides to get 10=2x10 = 2x. Finally, divide by 2 to find x=5x = 5.

Question 2

What is the solution to the equation 12x−3=14x+1\frac{1}{2}x - 3 = \frac{1}{4}x + 1?

  1. x=4x = 4
  2. x=8x = 8
  3. x=13x = 13
  4. x=16x = 16 (correct answer)
Explanation: To solve this equation, first eliminate the fractions by multiplying every term by the least common denominator, which is 4. This gives: 4(12x)−4(3)=4(14x)+4(1)4(\frac{1}{2}x) - 4(3) = 4(\frac{1}{4}x) + 4(1), which simplifies to 2x−12=x+42x - 12 = x + 4. Next, subtract xx from both sides to get x−12=4x - 12 = 4. Finally, add 12 to both sides to get x=16x = 16.

Question 3

Which of the following best describes the solution to the equation 4(y−1)−2y=2(y+3)4(y - 1) - 2y = 2(y + 3)?

  1. y=−5y = -5
  2. y=0y = 0
  3. All real numbers
  4. No solution (correct answer)
Explanation: First, simplify both sides of the equation. On the left, distribute the 4: 4y−4−2y4y - 4 - 2y, which combines to 2y−42y - 4. On the right, distribute the 2: 2y+62y + 6. The equation becomes 2y−4=2y+62y - 4 = 2y + 6. If you subtract 2y2y from both sides, you get −4=6-4 = 6, which is a false statement. Because the variables cancel out and the resulting statement is false, there is no value of yy that can make the equation true. Therefore, there is no solution.

Question 4

For what value of kk does the equation 7x−5=k(x−1)+3x7x - 5 = k(x - 1) + 3x have no solution?

  1. k=−3k = -3
  2. k=3k = 3
  3. k=4k = 4 (correct answer)
  4. k=5k = 5
Explanation: First, simplify the right side of the equation: kx−k+3xkx - k + 3x, which can be rewritten as (k+3)x−k(k+3)x - k. The full equation is 7x−5=(k+3)x−k7x - 5 = (k+3)x - k. For an equation to have no solution, the coefficients of the variable term must be equal, while the constant terms must be unequal. Equating the coefficients of xx gives 7=k+37 = k + 3, which means k=4k = 4. Now, check if the constants are unequal. The constants are -5 and -kk. If k=4k=4, the constants are -5 and -4, which are unequal. Therefore, when k=4k = 4, the equation has no solution.

Question 5

The perimeter of a rectangle is 54 centimeters. The length is 3 centimeters more than twice the width. What is the width of the rectangle in centimeters?

  1. 8 (correct answer)
  2. 12
  3. 19
  4. 25.5
Explanation: Let ww be the width. The length ll is 2w+32w + 3. The formula for the perimeter is P=2(l+w)P = 2(l + w). Substitute the given values: 54=2((2w+3)+w)54 = 2((2w + 3) + w). Simplify inside the parentheses: 54=2(3w+3)54 = 2(3w + 3). Distribute the 2: 54=6w+654 = 6w + 6. Subtract 6 from both sides: 48=6w48 = 6w. Divide by 6 to find the width: w=8w = 8.

Question 6

What is the solution to the equation 12−[3(a−1)−a]=512 - [3(a - 1) - a] = 5?

  1. a=−5a = -5
  2. a=2a = 2
  3. a=4a = 4
  4. a=5a = 5 (correct answer)
Explanation: First, simplify the expression inside the brackets. Distribute the 3: 3a−3−a3a - 3 - a, which simplifies to 2a−32a - 3. The equation becomes 12−[2a−3]=512 - [2a - 3] = 5. Next, distribute the negative sign: 12−2a+3=512 - 2a + 3 = 5. Combine the constants on the left: 15−2a=515 - 2a = 5. Subtract 15 from both sides: −2a=−10-2a = -10. Finally, divide by -2 to get a=5a = 5.

Question 7

If 4x−7=134x - 7 = 13, what is the value of the expression x−2x - 2?

  1. 3 (correct answer)
  2. 5
  3. 18
  4. 20
Explanation: This is a two-step problem. First, solve the equation for xx. Add 7 to both sides of 4x−7=134x - 7 = 13 to get 4x=204x = 20. Then, divide by 4 to get x=5x = 5. Second, substitute this value of xx into the expression x−2x - 2. This gives 5−2=35 - 2 = 3.

Question 8

What is the solution to the equation 9x−5=3(x+4)9x - 5 = 3(x + 4)?

  1. x=176x = \frac{17}{6} (correct answer)
  2. x=76x = \frac{7}{6}
  3. x=32x = \frac{3}{2}
  4. x=617x = \frac{6}{17}
Explanation: First, distribute the 3 on the right side: 9x−5=3x+129x - 5 = 3x + 12. Next, subtract 3x3x from both sides to get 6x−5=126x - 5 = 12. Then, add 5 to both sides to get 6x=176x = 17. Finally, divide by 6 to isolate xx: x=176x = \frac{17}{6}.

Question 9

What is the value of xx if x+73−x4=2\frac{x + 7}{3} - \frac{x}{4} = 2?

  1. x=−26x = -26
  2. x=−4x = -4 (correct answer)
  3. x=−47x = -\frac{4}{7}
  4. x=17x = 17
Explanation: To solve, multiply every term by the least common denominator of 3 and 4, which is 12. This yields: 12(x+73)−12(x4)=12(2)12(\frac{x + 7}{3}) - 12(\frac{x}{4}) = 12(2). Simplify: 4(x+7)−3x=244(x + 7) - 3x = 24. Distribute the 4: 4x+28−3x=244x + 28 - 3x = 24. Combine the xx terms on the left: x+28=24x + 28 = 24. Subtract 28 from both sides to find x=−4x = -4.

Question 10

What is the value of xx if 21=5(x−2)+4x21 = 5(x - 2) + 4x?

  1. x=119x = \frac{11}{9}
  2. x=3x = 3
  3. x=319x = \frac{31}{9} (correct answer)
  4. x=11x = 11
Explanation: First, simplify the right side of the equation. Distribute the 5: 21=5x−10+4x21 = 5x - 10 + 4x. Combine the xx terms: 21=9x−1021 = 9x - 10. Add 10 to both sides: 31=9x31 = 9x. Finally, divide by 9 to solve for xx: x=319x = \frac{31}{9}.

Question 11

What is the value of zz in the equation 0.5(z−6)=0.2z+30.5(z - 6) = 0.2z + 3?

  1. 0
  2. 11
  3. 15
  4. 20 (correct answer)
Explanation: First, distribute 0.5 on the left side: 0.5z−3=0.2z+30.5z - 3 = 0.2z + 3. Next, subtract 0.2z0.2z from both sides to get 0.3z−3=30.3z - 3 = 3. Then, add 3 to both sides: 0.3z=60.3z = 6. Finally, divide by 0.3: z=6/0.3=20z = 6 / 0.3 = 20.

Question 12

If four times a number is increased by 3, the result is the same as seven less than six times the number. What is the number?

  1. -2
  2. 0.4
  3. 2
  4. 5 (correct answer)
Explanation: Let the number be xx. Translate the sentence into an equation. 'Four times a number is increased by 3' is 4x+34x + 3. 'Seven less than six times the number' is 6x−76x - 7. Set them equal: 4x+3=6x−74x + 3 = 6x - 7. To solve, subtract 4x4x from both sides: 3=2x−73 = 2x - 7. Add 7 to both sides: 10=2x10 = 2x. Divide by 2: x=5x = 5.

Question 13

A plumber charges a flat fee of $65 for a house call, plus $45 per hour for labor. If the final bill was $267.50, for how many hours did the plumber work?

  1. 3.5
  2. 4.0
  3. 4.5 (correct answer)
  4. 5.9
Explanation: Let hh be the number of hours worked. The total cost is the flat fee plus the hourly charge, so the equation is 65+45h=267.5065 + 45h = 267.50. To solve for hh, first subtract 65 from both sides: 45h=202.5045h = 202.50. Then, divide by 45: h=202.5045=4.5h = \frac{202.50}{45} = 4.5. The plumber worked for 4.5 hours.

Question 14

The sum of three consecutive odd integers is 87. What is the value of the largest of these integers?

  1. 27
  2. 29
  3. 31 (correct answer)
  4. 33
Explanation: Let the three consecutive odd integers be represented by nn, n+2n + 2, and n+4n + 4. Their sum is 87, so the equation is n+(n+2)+(n+4)=87n + (n + 2) + (n + 4) = 87. Combining like terms gives 3n+6=873n + 6 = 87. Subtracting 6 from both sides gives 3n=813n = 81. Dividing by 3 gives n=27n = 27. This is the smallest integer. The question asks for the largest integer, which is n+4n + 4. So, the largest integer is 27+4=3127 + 4 = 31.

Question 15

If 35y+2=11\frac{3}{5}y + 2 = 11, what is the value of y+5y + 5?

  1. 9
  2. 15
  3. 18
  4. 20 (correct answer)
Explanation: First, solve for yy. Subtract 2 from both sides of the equation to get 35y=9\frac{3}{5}y = 9. To isolate yy, multiply both sides by the reciprocal of 35\frac{3}{5}, which is 53\frac{5}{3}. This gives y=9×53=15y = 9 \times \frac{5}{3} = 15. The question asks for the value of y+5y + 5, so substitute y=15y=15 into the expression: 15+5=2015 + 5 = 20.

Question 16

What is the solution to the equation 2x−15=x+34\frac{2x - 1}{5} = \frac{x + 3}{4}?

  1. x=113x = \frac{11}{3}
  2. x=193x = \frac{19}{3} (correct answer)
  3. x=11x = 11
  4. x=19x = 19
Explanation: To solve this proportion, you can cross-multiply. Multiply the numerator of the left fraction by the denominator of the right, and set it equal to the numerator of the right fraction multiplied by the denominator of the left: 4(2x−1)=5(x+3)4(2x - 1) = 5(x + 3). Distribute on both sides: 8x−4=5x+158x - 4 = 5x + 15. Subtract 5x5x from both sides: 3x−4=153x - 4 = 15. Add 4 to both sides: 3x=193x = 19. Divide by 3: x=193x = \frac{19}{3}.

Question 17

What is the solution to the equation 5(n−2)−(n+4)=3n−85(n - 2) - (n + 4) = 3n - 8?

  1. n=−22n = -22
  2. n=−2n = -2
  3. n=2n = 2
  4. n=6n = 6 (correct answer)
Explanation: First, distribute on the left side: 5n−10−n−4=3n−85n - 10 - n - 4 = 3n - 8. Be careful to distribute the negative sign to both terms in the parenthesis. Combine like terms on the left: 4n−14=3n−84n - 14 = 3n - 8. Subtract 3n3n from both sides: n−14=−8n - 14 = -8. Add 14 to both sides: n=6n = 6.

Question 18

Find the value of bb such that the equation 2(3x−1)+b=6x−22(3x - 1) + b = 6x - 2 has an infinite number of solutions.

  1. b=−2b = -2
  2. b=0b = 0 (correct answer)
  3. b=2b = 2
  4. b=6b = 6
Explanation: For an equation to have an infinite number of solutions, both sides of the equation must be identical. First, simplify the left side by distributing the 2: 6x−2+b=6x−26x - 2 + b = 6x - 2. To make the sides identical, the constant terms must be equal. Here, we must have −2+b=−2-2 + b = -2. Adding 2 to both sides gives b=0b = 0.

Question 19

Which of the following best describes the solution to the equation −(w+5)+3w=2(w−3)+1-(w + 5) + 3w = 2(w - 3) + 1?

  1. w=0w = 0
  2. w=5w = 5
  3. No solution
  4. All real numbers (correct answer)
Explanation: First, simplify both sides of the equation. On the left, distribute the negative sign: −w−5+3w-w - 5 + 3w, which combines to 2w−52w - 5. On the right, distribute the 2: 2w−6+12w - 6 + 1, which combines to 2w−52w - 5. The equation becomes 2w−5=2w−52w - 5 = 2w - 5. This statement is always true, regardless of the value of ww. Because the two sides are identical, any real number substituted for ww will result in a true statement. Therefore, the solution is all real numbers.

Question 20

What is the solution to the equation 8−32(2x−4)=58 - \frac{3}{2}(2x - 4) = 5?

  1. x=3x = 3 (correct answer)
  2. x=−13x = -\frac{1}{3}
  3. x=73x = \frac{7}{3}
  4. x=−1x = -1
Explanation: First, distribute −32-\frac{3}{2} to both terms inside the parentheses: 8+(−32)(2x)+(−32)(−4)=58 + (-\frac{3}{2})(2x) + (-\frac{3}{2})(-4) = 5. This simplifies to 8−3x+6=58 - 3x + 6 = 5. Combine the constant terms on the left: 14−3x=514 - 3x = 5. Subtract 14 from both sides: −3x=−9-3x = -9. Finally, divide by -3 to get x=3x = 3.