Middle School Math Quiz: Solve Two Step Linear Equations
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Solve Two Step Linear EquationsQuestion 1 of 20

The equation 4(2x−3)=6x+144(2x - 3) = 6x + 14 represents a real-world situation where costs must be equal. After solving algebraically to get x=13x = 13, which arithmetic verification correctly confirms this solution?

Left side: 4(2⋅13−3)=4(20)=804(2 \cdot 13 - 3) = 4(20) = 80; Right side: 6⋅13+14=926 \cdot 13 + 14 = 92
Left side: 4(2⋅13−3)=4(23)=924(2 \cdot 13 - 3) = 4(23) = 92; Right side: 6⋅13+14=866 \cdot 13 + 14 = 86
Left side: 4(2⋅13−3)=4(26)=1044(2 \cdot 13 - 3) = 4(26) = 104; Right side: 6⋅13+14=926 \cdot 13 + 14 = 92
Left side: 4(2⋅13−3)=4(23)=924(2 \cdot 13 - 3) = 4(23) = 92; Right side: 6⋅13+14=926 \cdot 13 + 14 = 92
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Middle School Math Quiz

Middle School Math Quiz: Solve Two Step Linear Equations

Practice Solve Two Step Linear Equations in Middle School 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 Solve Two Step Linear Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School 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

The equation 4(2x−3)=6x+144(2x - 3) = 6x + 14 represents a real-world situation where costs must be equal. After solving algebraically to get x=13x = 13, which arithmetic verification correctly confirms this solution?

  1. Left side: 4(2⋅13−3)=4(20)=804(2 \cdot 13 - 3) = 4(20) = 80; Right side: 6⋅13+14=926 \cdot 13 + 14 = 92
  2. Left side: 4(2⋅13−3)=4(23)=924(2 \cdot 13 - 3) = 4(23) = 92; Right side: 6⋅13+14=866 \cdot 13 + 14 = 86
  3. Left side: 4(2⋅13−3)=4(26)=1044(2 \cdot 13 - 3) = 4(26) = 104; Right side: 6⋅13+14=926 \cdot 13 + 14 = 92
  4. Left side: 4(2⋅13−3)=4(23)=924(2 \cdot 13 - 3) = 4(23) = 92; Right side: 6⋅13+14=926 \cdot 13 + 14 = 92 (correct answer)
Explanation: When you have an algebraic equation and need to verify a solution, you substitute the proposed value back into the original equation and check that both sides are equal. This confirmation step is crucial because it catches any algebraic errors you might have made while solving. To verify x=13x = 13 in the equation 4(2x−3)=6x+144(2x - 3) = 6x + 14, you need to carefully substitute 13 for xx and evaluate each side separately. For the left side: 4(2x−3)=4(2⋅13−3)=4(26−3)=4(23)=924(2x - 3) = 4(2 \cdot 13 - 3) = 4(26 - 3) = 4(23) = 92 For the right side: 6x+14=6⋅13+14=78+14=926x + 14 = 6 \cdot 13 + 14 = 78 + 14 = 92 Since both sides equal 92, the solution x=13x = 13 is correct. This matches answer choice D. Looking at the wrong answers: Choice A makes an order of operations error on the left side, calculating 2⋅13−32 \cdot 13 - 3 as 20 instead of 23, leading to 80 instead of 92. Choice B correctly calculates the left side as 92 but makes an arithmetic error on the right side, getting 86 instead of 92. Choice C makes a different error on the left side, somehow getting 26 instead of 23 inside the parentheses. Remember: verification problems test your arithmetic precision more than your algebra skills. Work slowly through the order of operations, double-check your basic arithmetic, and make sure both sides of the equation give you the same final value.

Question 2

A taxi company charges $3.50 for the first mile and $2.25 for each additional mile. If the total fare for a trip was $25.75, which equation correctly represents this situation, and how many miles was the trip?

  1. 3.50+2.25x=25.753.50 + 2.25x = 25.75; the trip was 9.9 miles total
  2. 3.50+2.25(x−1)=25.753.50 + 2.25(x - 1) = 25.75; the trip was 10.9 miles total
  3. 3.50+2.25(x−1)=25.753.50 + 2.25(x - 1) = 25.75; the trip was 11 miles total (correct answer)
  4. 3.50x+2.25(x−1)=25.753.50x + 2.25(x - 1) = 25.75; the trip was 6.2 miles total
Explanation: Since the first mile costs $3.50 and additional miles cost $2.25 each, if the total trip is $xmiles,therearemiles, there are(x-1)additionalmiles.Thecorrectequationisadditional miles. The correct equation is3.50 + 2.25(x-1) = 25.75.Solving:. Solving: 2.25(x-1) = 22.25,so, so x-1 = 22.25 ÷ 2.25 = 9.89.Sincedistancemustbeawholenumberofmiles,. Since distance must be a whole number of miles, x-1 = 10,giving, giving x = 11$ miles. Choice A uses the wrong equation structure. Choice B has the right equation but wrong calculation. Choice D incorrectly charges $3.50 per mile for all miles.

Question 3

A movie theater has two pricing options for groups. Option A charges $12 per person. Option B charges a $36 group fee plus $8 per person. For what group size do both options cost exactly the same amount?

  1. 8 people, with both options costing $96 total
  2. 9 people, with both options costing $108 total (correct answer)
  3. 10 people, with both options costing $120 total
  4. 11 people, with both options costing $132 total
Explanation: Let nn be the number of people. Option A costs 12n12n and Option B costs 36+8n36 + 8n. Setting them equal: 12n=36+8n12n = 36 + 8n, so 4n=364n = 36 and n=9n = 9. Check: Option A = 12(9)=10812(9) = 108 and Option B = 36+8(9)=36+72=10836 + 8(9) = 36 + 72 = 108. Both options cost exactly $108 for 9 people. The other choices show incorrect group sizes that don't result in equal costs.

Question 4

A bike rental costs $12 per hour plus a one-time $6 helmet fee. If the total cost was $78, how many hours did the bike rental last?

  1. 8 hours
  2. 5 hours
  3. 6 hours (correct answer)
  4. 7 hours
Explanation: This problem tests solving two-step equations from word problems in the form px+q=rpx + q = r, where we multiply the variable then add a constant, using inverse operations. The bike rental costs $12 per hour (variable cost) plus a $6 helmet fee (fixed cost), totaling $78, so we write 12h+6=7812h + 6 = 78 where h is the number of hours. To solve: (1) subtract 6 from both sides to isolate the variable term (12h=7212h = 72), then (2) divide by 12 to isolate h (h=72÷12=6h = 72 ÷ 12 = 6). The rental lasted 6 hours. Common errors include: stopping after one step (getting 72 as the answer), reversing operations (dividing first: 78÷12=6.578 ÷ 12 = 6.5, then subtracting 6 = 0.50.5), or arithmetic mistakes (72÷12=772 ÷ 12 = 7). Strategy: identify the equation form from context (hourly rate × hours + helmet fee = total), apply inverse operations in reverse order (subtract then divide), and verify by substituting back (12×6+6=72+6=78✓12 × 6 + 6 = 72 + 6 = 78 ✓).

Question 5

A school fundraiser sells tubs of cookie dough for $8.75 each. The club also pays a one-time booth rental fee of $10.00. If the total cost was $80.00, how many tubs did they buy? Solve 8.75x+10=808.75x+10=80.

  1. x=70x=70
  2. x=8x=8 (correct answer)
  3. x=9x=9
  4. x=6x=6
Explanation: This question tests solving two-step equations from word problems in the px + q = r form, where you multiply a variable by a coefficient and then add a constant, using inverse operations to isolate the variable. To solve px + q = r, first subtract q from both sides to isolate the variable term, for example, 8.75x + 10 = 80 becomes 8.75x = 70, then divide both sides by p to isolate the variable, so 8.75x ÷ 8.75 = 70 ÷ 8.75 gives x = 8; for the other form p(x + q) = r, divide by p first then subtract q, and always verify by substituting back, like 8.75 × 8 + 10 = 70 + 10 = 80, which checks out in the context of cookie dough tubs at $8.75 each plus $10 fee totaling $80 for x tubs. For this specific problem, the equation is given as 8.75x + 10 = 80, subtract 10 to get 8.75x = 70, divide by 8.75 to find x = 8, verify 8.75 × 8 + 10 = 80, and interpret as 8 tubs bought. The correct two-step process yields x = 8, which is choice A. Common errors include subtracting only and forgetting to divide (x = 70, choice C), reversing order by dividing first (80 ÷ 8.75 ≈ 9.14 then subtract 10, nonsensical), sign errors like adding instead (8.75x = 90), arithmetic mistakes (70 ÷ 8.75 = 9 or 6), or wrong setup though it's provided. Strategy tips include identifying the px + q = r form from per-tub cost plus fixed fee, applying inverse operations in reverse (subtract then divide), maintaining equality by doing the same to both sides, verifying by substitution and context sense (8 tubs at $8.75 is $70 plus $10 totals $80, reasonable), and checking reasonableness. Compared to arithmetic working backwards (80 - 10 = 70, 70 ÷ 8.75 = 8), algebra generalizes for any total; avoid mistakes like stopping after one step, wrong order, sign errors, or mismatched setup.

Question 6

Compare methods: A streaming service charges $9.75 per month plus a one-time $4.50 fee. The total paid was $53.25. How many months were paid for? (You could solve algebraically or by working backward.)

  1. 7 months
  2. 6 months
  3. 4 months
  4. 5 months (correct answer)
Explanation: This problem tests solving two-step equations from word problems in the form px+q=rpx + q = r, where we multiply the variable then add a constant, using inverse operations. The streaming service costs $9.75 per month (variable cost) plus a $4.50 fee (fixed cost), totaling $53.25, so we write 9.75m+4.50=53.259.75m + 4.50 = 53.25 where m is the number of months. To solve algebraically: (1) subtract 4.50 from both sides (9.75m=48.759.75m = 48.75), then (2) divide by 9.75 (m=48.75÷9.75=5m = 48.75 ÷ 9.75 = 5). Working backward gives the same result: \53.25 - $4.50 = $48.75,then, then $48.75 ÷ $9.75 = 5$ months. Common errors include: stopping after one step, reversing operations, or arithmetic mistakes with decimals. Both methods—algebraic equation solving and working backward—yield 5 months, demonstrating that algebra generalizes the arithmetic approach of undoing operations in reverse order.

Question 7

Verify a solution: A tutoring session costs $18 per hour plus a $6 materials fee. The total bill was $78. Which value of h correctly solves 18h+6=78 and fits the situation?

  1. h=4 (correct answer)
  2. h=7/2
  3. h=3
  4. h=13/3
Explanation: Subtracting 6 from both sides of 18h + 6 = 78 gives 18h = 72, and dividing by 18 gives h = 4, matching choice A. Checking: 18 x 4 + 6 = 72 + 6 = 78, which fits the situation of 4 hours tutored. Choices B, C, and D don't satisfy the equation: substituting each back in gives totals of $69, $60, and $84 instead of the required $78.

Question 8

A class is making gift bags. Each bag needs 33 stickers, and the teacher adds 55 extra stickers for mistakes. If there are 4747 stickers total, how many gift bags can be made? (Model with 3x+5=473x+5=47.)

  1. x=16x=16
  2. x=42x=42
  3. x=12x=12
  4. x=14x=14 (correct answer)
Explanation: This question tests solving two-step equations from word problems in the px + q = r form, where you multiply a variable by a coefficient and then add a constant, using inverse operations to isolate the variable. To solve px + q = r, first subtract q from both sides to isolate the variable term, for example, 3x + 5 = 47 becomes 3x = 42, then divide both sides by p to isolate the variable, so 3x / 3 = 42 / 3 gives x = 14; always verify by substituting back, like 3 × 14 + 5 = 42 + 5 = 47, which checks out. For this specific problem, use the given model 3x + 5 = 47, subtract 5 to get 3x = 42, divide by 3 to find x = 14, verify 3 × 14 + 5 = 47, and interpret as 14 gift bags can be made. The correct two-step process yields x = 14, which is choice A. Common errors include dividing first (47 / 3 ≈ 15.667, subtract 5 ≈ 10.667 nonsense), arithmetic mistakes (42 / 3 = 12 or 16 wrongly), one-step only (47 - 5 = 42, forget divide), sign error (3x = 52 by adding), or setup wrong (5x + 3 = 47). Strategy: identify the equation form px + q = r from the context, apply inverse operations in reverse order (subtract then divide to undo add then multiply), maintain equality by doing the same to both sides, verify by substituting back to ensure it satisfies the equation and makes sense (14 bags need 42 stickers plus 5 extra totals 47), and check reasonableness (total minus extra divisible by 3). Comparing to arithmetic, work backwards: 47 - 5 = 42, 42 / 3 = 14, same answer; algebra generalizes for any total; avoid mistakes like wrong order or miscalculation.

Question 9

Solve the equation 3(x+4)=273(x+4)=27.

  1. x=5x=5 (correct answer)
  2. x=13x=13
  3. x=7x=7
  4. x=3x=3
Explanation: This question tests solving two-step equations in the p(x + q) = r form, where you multiply a grouped expression by a coefficient, using inverse operations to isolate the variable. To solve p(x + q) = r, first divide both sides by p to isolate the grouped term, for example, 3(x + 4) = 27 becomes x + 4 = 9, then subtract q from both sides to isolate the variable, so x = 9 - 4 = 5; always verify by substituting back, like 3(5 + 4) = 3 × 9 = 27, which checks out. For this specific problem, start with 3(x + 4) = 27, divide by 3 to get x + 4 = 9, subtract 4 to find x = 5, and verify 3(5 + 4) = 27. The correct two-step process yields x = 5, which is choice A. Common errors include distributing wrongly (3x + 4 = 27, then mistakes), order reversed (subtract 4 from 27 = 23, divide by 3 ≈ 7.67 nonsense), arithmetic error (27 / 3 = 8, 8 - 4 = 4), or expanding incorrectly (3x + 12 = 27). Strategy: identify the equation form p(x + q) = r, apply inverse operations in reverse order (divide then subtract to undo multiply after add), maintain equality by doing the same to both sides, verify by substituting back to ensure it satisfies the equation, and check reasonableness (5 + 4 = 9, times 3 is 27). Comparing to arithmetic, work backwards: 27 / 3 = 9, 9 - 4 = 5, same answer; algebra generalizes for any right side; avoid mistakes like wrong order or distribution errors.

Question 10

A water bottle costs $3.25 and there is a fixed tax of $1.50 added to the total purchase. If the total cost was $27.50, how many water bottles were bought? Set up and solve 3.25b+1.50=27.503.25b+1.50=27.50.

  1. b=8b=8 (correct answer)
  2. b=26b=26
  3. b=7b=7
  4. b=9b=9
Explanation: This question tests solving two-step equations from word problems in the px+q=rpx + q = r form, where you multiply a variable by a coefficient and then add a constant, using inverse operations to isolate the variable. To solve px+q=rpx + q = r, first subtract qq from both sides to isolate the variable term, for example, 3.25b+1.5=27.53.25b + 1.5 = 27.5 becomes 3.25b=263.25b = 26, then divide both sides by pp to isolate the variable, so 3.25b÷3.25=26÷3.253.25b \div 3.25 = 26 \div 3.25 gives b=8b = 8; for the other form p(x+q)=rp(x + q) = r, divide by pp first then subtract qq, and always verify by substituting back, like 3.25×8+1.5=26+1.5=27.53.25 \times 8 + 1.5 = 26 + 1.5 = 27.5, which checks out in the context of water bottles at 3.253.25 each plus 1.501.50 tax totaling 27.5027.50 for bb bottles. For this specific problem, the equation is given as 3.25b+1.5=27.53.25b + 1.5 = 27.5, subtract 1.51.5 to get 3.25b=263.25b = 26, divide by 3.253.25 to find b=8b = 8, verify 3.25×8+1.5=27.53.25 \times 8 + 1.5 = 27.5, and interpret as 88 water bottles bought. The correct two-step process yields b=8b = 8, which is choice A. Common errors include subtracting only and forgetting to divide (b=26b = 26, choice D), reversing order by dividing first (27.5÷3.25≈8.4627.5 \div 3.25 \approx 8.46 then subtract 1.51.5, nonsensical), sign errors like adding instead (3.25b=293.25b = 29), arithmetic mistakes (26÷3.25=926 \div 3.25 = 9 or 77), or wrong setup though it's provided. Strategy tips include identifying the px+q=rpx + q = r form from per-bottle cost plus fixed tax, applying inverse operations in reverse (subtract then divide), maintaining equality by doing the same to both sides, verifying by substitution and context sense (88 bottles at 3.253.25 is 2626 plus 1.501.50 totals 27.5027.50, reasonable), and checking reasonableness. Compared to arithmetic working backwards (27.5−1.5=2627.5 - 1.5 = 26, 26÷3.25=826 \div 3.25 = 8), algebra generalizes for any total; avoid mistakes like stopping after one step, wrong order, sign errors, or mismatched setup.

Question 11

A streaming app charges $7.50 per month plus a one-time sign-up fee of $4.50. If Maya paid a total of $49.50, how many months did she pay for? Write and solve an equation of the form px+q=r.

  1. m=6.6
  2. m=5
  3. m=6 (correct answer)
  4. m=7
Explanation: The equation is 7.5m + 4.5 = 49.5. Subtracting 4.5 from both sides gives 7.5m = 45, and dividing by 7.5 gives m = 6, matching choice C. Checking: 7.5 x 6 + 4.5 = 45 + 4.5 = 49.5, which fits the context of 6 months of subscription. Choice A (6.6) comes from dividing 49.5 by 7.5 first instead of subtracting the fee, and choices B and D don't satisfy the equation when substituted back in.

Question 12

A hobby store sells refill packs for $5 each. A science kit comes with some number of paid refill packs, plus 2 bonus packs added for free. The kit's total advertised value, treating all packs (paid and bonus) at $5 each, is $45. If $prepresentsthenumberofpaidrefillpacks,thiscanbemodeledbyrepresents the number of paid refill packs, this can be modeled by5(p+2)=45.Solvefor. Solve for p$.

  1. p=9p=9
  2. p=7p=7 (correct answer)
  3. p=11p=11
  4. p=5p=5
Explanation: To solve 5(p+2)=45, first divide both sides by 5: p+2=9. Then subtract 2 from both sides: p=7, matching choice B. Verify: 5(7+2)=5x9=45, which checks out. Choice A stops after dividing but forgets to subtract 2, leaving p+2's value (9) as the final answer. Choice C divides 45 by 5 to get 9, then adds 2 instead of subtracting, giving 11. Choice D makes an arithmetic error, subtracting incorrectly to arrive at 5.

Question 13

A class is making snack bags. Each bag has the same number of pretzels. After making 6 bags, there are 3 pretzels left over, and the class started with 51 pretzels. Let xx be the number of pretzels in each bag. Which equation matches the situation, and what is xx?

(Equation form: px+q=rpx+q=r)

  1. 6x−3=516x-3=51, so x=9x=9
  2. 3x+6=513x+6=51, so x=15x=15
  3. 51x+3=651x+3=6, so x=117x=\tfrac{1}{17}
  4. 6x+3=516x+3=51, so x=8x=8 (correct answer)
Explanation: This problem tests solving two-step equations from word problems in the form px+q=r, where we multiply the variable then add a constant, using inverse operations. The class makes 6 bags with x pretzels each (6x total) plus 3 leftover pretzels equals 51 total pretzels, giving equation 6x + 3 = 51. To solve: (1) subtract 3 from both sides to isolate the variable term (6x = 48), then (2) divide by 6 to isolate x (x = 48 ÷ 6 = 8). Each bag has 8 pretzels, matching answer choice A. Common errors include: reversing the equation setup (51x + 3 = 6 as in choice C), swapping coefficients (3x + 6 = 51 as in choice D), or using subtraction instead of addition for leftovers (6x - 3 = 51 as in choice B). Strategy: identify what's multiplied (bags × pretzels per bag) and what's added (leftovers), set up equation matching the context, apply inverse operations, and verify (6×8+3=48+3=51✓).

Question 14

At a sports store, each item costs $4. You are buying one identical item for each of your friends, plus 2 extra items for yourself and a backup. If the total cost was $36, how many friends were you shopping for?

  1. 77 friends (correct answer)
  2. 99 friends
  3. 1111 friends
  4. 55 friends
Explanation: Since you're buying one item for each friend plus 2 extra items for yourself and a backup, the total number of items is x + 2, where x is the number of friends. The equation for the total cost is 4(x + 2) = 36. Dividing both sides by 4 gives x + 2 = 9, and subtracting 2 gives x = 7. Checking: 4(7 + 2) = 4(9) = 36, which matches. Choice B comes from stopping after finding the total number of items, 9, without subtracting the 2 extra. Choice C and choice D come from errors in the order of the division and subtraction steps.

Question 15

A bookstore offers a membership program. The annual membership fee is $24, and members get a 20% discount on all purchases. If a member spent a total of $156 last year (including the membership fee), what was the original price of the books before the discount?

  1. $165.00 (correct answer)
  2. $168.75
  3. $172.50
  4. $180.00
Explanation: Let x be the original price of the books. After the fee and discount, the member pays 24 + 0.8x = 156. Solving: subtract 24 to get 0.8x = 132, then divide by 0.8 to get x = 165, matching choice A. None of the other amounts satisfy this equation: plugging 168.75, 172.50, or 180 back into 24 + 0.8x gives totals of $159, $162, and $168 respectively, not the required $156.

Question 16

Solve the equation 15x+6=96.

  1. x=7
  2. x=5.6
  3. x=90
  4. x=6 (correct answer)
Explanation: Subtracting 6 from both sides of 15x + 6 = 96 gives 15x = 90, and dividing by 15 gives x = 6, matching choice D. Checking: 15 x 6 + 6 = 90 + 6 = 96. Choice B (5.6) and choice A (7) both come from arithmetic slips in the division step, and choice C (90) stops after subtracting but forgets to divide by 15.

Question 17

A museum charges $12 for each ticket and adds a one-time online processing fee of $3. If a group paid $75 total, how many tickets did they buy? Solve 12t+3=75.

  1. t=6.25
  2. t=6 (correct answer)
  3. t=5
  4. t=72
Explanation: Subtracting 3 from both sides of 12t + 3 = 75 gives 12t = 72, and dividing by 12 gives t = 6, matching choice B. Checking: 12 x 6 + 3 = 72 + 3 = 75, which fits 6 tickets purchased. Choice A (6.25) comes from dividing 75 by 12 first instead of subtracting the fee. Choice C (5) is an arithmetic slip in the division, and choice D (72) stops after subtracting but forgets to divide by 12.

Question 18

A snack shop sells party bags. Each bag includes some number of paid snack packs, plus 3 bonus packs added for free. The shop values every pack, paid or bonus, at $4 each, and the total value of one bag is $36. If $xrepresentsthenumberofpaidsnackpacks,thiscanbemodeledbyrepresents the number of paid snack packs, this can be modeled by4(x+3)=36.Solvefor. Solve for x$.

  1. x=3x=3
  2. x=12x=12
  3. x=6x=6 (correct answer)
  4. x=9x=9
Explanation: To solve 4(x+3)=36, first divide both sides by 4: x+3=9. Then subtract 3 from both sides: x=6, matching choice C. Verify: 4(6+3)=4x9=36, which checks out. Choice A comes from an arithmetic slip. Choice B stops after dividing but forgets to subtract 3, leaving the value of x+3 (9) plus an extra step gone wrong. Choice D divides 36 by 4 to get 9, then adds 3 instead of subtracting, giving 12 mistakenly recorded, or represents a similar addition error.

Question 19

Solve the equation 5(x+3)=405(x+3)=40.

  1. x=8x=8
  2. x=37x=37
  3. x=5x=5 (correct answer)
  4. x=11x=11
Explanation: Dividing both sides by 5 first gives x + 3 = 8. Subtracting 3 from both sides gives x = 5. Checking: 5(5+3) = 5(8) = 40, which matches. Choice A stops after dividing by 5 and forgets to subtract 3 to finish isolating x. Choice B comes from incorrectly expanding the expression as 5x + 3 = 40, leading to 5x = 37, then stopping without dividing by 5. Choice D comes from adding 3 instead of subtracting it after dividing by 5.

Question 20

Compare methods: A student says the equation for this situation is 7x+2=447x+2=44: "Each notebook costs $7, and there is a $2 fee for the whole purchase. The total was $44." What is the correct number of notebooks?

  1. x=7x=7
  2. x=42x=42
  3. x=5x=5
  4. x=6x=6 (correct answer)
Explanation: Starting with the equation 7x plus 2 equals 44, subtracting 2 from both sides gives 7x equals 42, and dividing both sides by 7 gives x equals 6, matching choice D. Choice A, x equals 7, does not satisfy the equation, since 7 times 7 plus 2 equals 51, not 44. Choice B, x equals 42, comes from stopping after subtracting 2 and forgetting to divide by 7. Choice C, x equals 5, comes from an arithmetic slip when dividing 42 by 7. Checking the answer by substitution, 7 times 6 plus 2 equals 42 plus 2, which equals 44, confirms that x equals 6 is correct.