Praxis Math Quiz: Solve Linear Equations
20 questions · exam conditions
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Solve Linear EquationsQuestion 1 of 20

An investment of $1,200 earns simple interest. After 5 years, the total value of the investment is $1,500. Using the simple interest formula I=PrtI = Prt, where II is interest, PP is principal, rr is the annual rate, and tt is time in years, what was the annual interest rate?

4%
5%
20%
25%
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Praxis Math Quiz

Praxis Math Quiz: Solve Linear Equations

Practice Solve Linear Equations in Praxis 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 Linear Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis 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.

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Question 1

An investment of $1,200 earns simple interest. After 5 years, the total value of the investment is $1,500. Using the simple interest formula I=PrtI = Prt, where II is interest, PP is principal, rr is the annual rate, and tt is time in years, what was the annual interest rate?

  1. 4%
  2. 5% (correct answer)
  3. 20%
  4. 25%
Explanation: First, calculate the total interest earned (II) by subtracting the principal (PP) from the final amount: (I = 1,500−1,500 - 1,200 = 300\). Now, use the formula I = PrtwithwithI=300,, P=1200,and, and t=5.Theequationis. The equation is 300 = 1200 \times r \times 5.Simplifytherightside:. Simplify the right side: 300 = 6000r.Tofindtherate. To find the rate r,dividebothsidesby6000:, divide both sides by 6000: r = \frac{300}{6000} = \frac{3}{60} = \frac{1}{20} = 0.05$. To express this as a percentage, multiply by 100. The annual interest rate is 5%.

Question 2

A cell phone plan costs $30 per month and includes 2 gigabytes (GB) of data. Each additional gigabyte of data costs $10. If a customer's bill was $75 for one month, not including taxes, how many total gigabytes of data did the customer use?

  1. 4.5 GB
  2. 6.5 GB (correct answer)
  3. 7.5 GB
  4. 10.5 GB
Explanation: Let gg be the number of additional gigabytes used. The cost for additional data is 10g10g. The total bill is the base cost plus the additional data cost: 30+10g=7530 + 10g = 75. To find gg, first subtract 30 from both sides: 10g=4510g = 45. Then divide by 10: g=4.5g = 4.5. This represents the additional gigabytes. The question asks for the total gigabytes used, which is the included 2 GB plus the additional 4.5 GB. Total data = 2+4.5=6.52 + 4.5 = 6.5 GB.

Question 3

The equation A=P(1+rt)A = P(1+rt) gives the total amount AA in an account with principal PP, annual interest rate rr, and time in years tt. If an account grows to $5,250 in 10 years with an initial principal of $3,000, what is the value of rr?

  1. 0.05
  2. 0.075 (correct answer)
  3. 0.175
  4. 0.75
Explanation: Substitute the given values into the equation: 5250=3000(1+r⋅10)5250 = 3000(1 + r \cdot 10). First, divide both sides by 3000: 52503000=1+10r\frac{5250}{3000} = 1 + 10r. The fraction simplifies to 1.751.75. So, 1.75=1+10r1.75 = 1 + 10r. Next, subtract 1 from both sides: 0.75=10r0.75 = 10r. Finally, divide by 10 to solve for rr: r=0.7510=0.075r = \frac{0.75}{10} = 0.075.

Question 4

Maria is twice as old as her brother, Sam. In 6 years, the sum of their ages will be 39. How old is Sam now?

  1. 7
  2. 9 (correct answer)
  3. 13
  4. 15
Explanation: Let Sam's current age be SS. Then Maria's current age is 2S2S. In 6 years, Sam's age will be S+6S+6 and Maria's age will be 2S+62S+6. The sum of their ages in 6 years will be 39, so (S+6)+(2S+6)=39(S+6) + (2S+6) = 39. Combine like terms: 3S+12=393S + 12 = 39. Subtract 12 from both sides: 3S=273S = 27. Divide by 3: S=9S = 9. Sam is currently 9 years old.

Question 5

If 3x−(4−x)=2(x−5)3x - (4 - x) = 2(x - 5), what is the value of x+3x+3?

  1. -3
  2. 0 (correct answer)
  3. 3
  4. 6
Explanation: First, solve the equation for xx. Distribute the negative sign on the left and the 2 on the right: 3x−4+x=2x−103x - 4 + x = 2x - 10. Combine like terms on the left: 4x−4=2x−104x - 4 = 2x - 10. Subtract 2x2x from both sides: 2x−4=−102x - 4 = -10. Add 4 to both sides: 2x=−62x = -6. Divide by 2: x=−3x = -3. The question asks for the value of x+3x+3, not xx. Substitute x=−3x = -3 into the expression: −3+3=0-3 + 3 = 0.

Question 6

For what value of cc will the equation 5y−7=c(y−1)+2y5y - 7 = c(y-1) + 2y have no solution?

  1. -7
  2. 2
  3. 3 (correct answer)
  4. 5
Explanation: A linear equation has no solution if the variable terms cancel out but the constant terms are not equal. First, simplify the right side of the equation: 5y−7=cy−c+2y5y - 7 = cy - c + 2y. Combine the yy terms on the right: 5y−7=(c+2)y−c5y - 7 = (c+2)y - c. For the equation to have no solution, the coefficients of yy on both sides must be equal, so 5=c+25 = c+2. Solving for cc gives c=3c = 3. If c=3c=3, the equation becomes 5y−7=5y−35y - 7 = 5y - 3, which simplifies to −7=−3-7 = -3, a contradiction. Thus, when c=3c=3, there is no solution.

Question 7

The sum of four consecutive even integers is 196. What is the product of the smallest and largest of these integers?

  1. 98
  2. 196
  3. 2392 (correct answer)
  4. 2548
Explanation: Let the four consecutive even integers be nn, n+2n+2, n+4n+4, and n+6n+6. Their sum is n+(n+2)+(n+4)+(n+6)=196n + (n+2) + (n+4) + (n+6) = 196. Combine like terms: 4n+12=1964n + 12 = 196. Subtract 12 from both sides: 4n=1844n = 184. Divide by 4: n=46n = 46. This is the smallest integer. The four integers are 46, 48, 50, and 52. The question asks for the product of the smallest (46) and the largest (52). The product is 46×52=239246 \times 52 = 2392.

Question 8

If a number is doubled and then decreased by 7, the result is the same as if the number were increased by 5. What is the number?

  1. -12
  2. 4
  3. 12 (correct answer)
  4. 19
Explanation: Let the number be xx. Translating the words into an equation gives: 2x−7=x+52x - 7 = x + 5. To solve for xx, subtract xx from both sides: x−7=5x - 7 = 5. Then, add 7 to both sides: x=12x = 12. The number is 12.

Question 9

What is the solution to the equation 4[x−2(x−3)]=84[x - 2(x-3)] = 8?

  1. -8
  2. -2
  3. 4 (correct answer)
  4. 10
Explanation: To solve this equation, work from the inside out. First, distribute the -2 inside the brackets: 4[x−2x+6]=84[x - 2x + 6] = 8. Combine the xx terms inside the brackets: 4[−x+6]=84[-x + 6] = 8. Next, distribute the 4: −4x+24=8-4x + 24 = 8. Subtract 24 from both sides: −4x=−16-4x = -16. Finally, divide by -4: x=4x = 4. Alternatively, one could divide both sides by 4 first: x−2(x−3)=2x - 2(x-3) = 2, which leads to the same result.

Question 10

Solve for xx in the equation x3−x−24=1\frac{x}{3} - \frac{x-2}{4} = 1.

  1. -5
  2. 6 (correct answer)
  3. 10
  4. 18
Explanation: To clear the fractions, multiply the entire equation by the least common denominator of 3 and 4, which is 12. 12(x3)−12(x−24)=12(1)12(\frac{x}{3}) - 12(\frac{x-2}{4}) = 12(1). This simplifies to 4x−3(x−2)=124x - 3(x-2) = 12. Distribute the -3: 4x−3x+6=124x - 3x + 6 = 12. Combine the xx terms: x+6=12x + 6 = 12. Subtract 6 from both sides to get x=6x = 6.

Question 11

What is the solution for aa in the equation 3a−12+1=3a+42\frac{3a-1}{2} + 1 = \frac{3a+4}{2}?

  1. a=−43a = -\frac{4}{3}
  2. a=0a = 0
  3. There is no solution. (correct answer)
  4. The solution is all real numbers.
Explanation: To solve the equation, first eliminate the denominators by multiplying every term by 2: 2(3a−12)+2(1)=2(3a+42)2(\frac{3a-1}{2}) + 2(1) = 2(\frac{3a+4}{2}). This simplifies to (3a−1)+2=3a+4(3a-1) + 2 = 3a+4. Combine the constants on the left side: 3a+1=3a+43a + 1 = 3a + 4. If we subtract 3a3a from both sides, we are left with 1=41 = 4, which is a false statement. This means the original equation is a contradiction and has no solution.

Question 12

If 12x+13x+14x=26\frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x = 26, what is the value of xx?

  1. 2
  2. 12
  3. 24 (correct answer)
  4. 26
Explanation: To solve for xx, first find a common denominator for the fractions, which is 12. Rewrite the equation with the common denominator: 612x+412x+312x=26\frac{6}{12}x + \frac{4}{12}x + \frac{3}{12}x = 26. Combine the terms on the left: 1312x=26\frac{13}{12}x = 26. To isolate xx, multiply both sides by the reciprocal of 1312\frac{13}{12}, which is 1213\frac{12}{13}: x=26×1213x = 26 \times \frac{12}{13}. Since 26/13=226/13 = 2, the equation becomes x=2×12=24x = 2 \times 12 = 24.

Question 13

The equation for converting temperature from Celsius (CC) to Fahrenheit (FF) is F=95C+32F = \frac{9}{5}C + 32. Which of the following equations correctly expresses CC in terms of FF?

  1. C=59(F−32)C = \frac{5}{9}(F - 32) (correct answer)
  2. C=95(F−32)C = \frac{9}{5}(F - 32)
  3. C=59F−32C = \frac{5}{9}F - 32
  4. C=59F+32C = \frac{5}{9}F + 32
Explanation: To solve the equation F=95C+32F = \frac{9}{5}C + 32 for CC, we must isolate CC. First, subtract 32 from both sides: F−32=95CF - 32 = \frac{9}{5}C. Next, to get CC by itself, multiply both sides by the reciprocal of 95\frac{9}{5}, which is 59\frac{5}{9}. This gives 59(F−32)=C\frac{5}{9}(F - 32) = C. Thus, C=59(F−32)C = \frac{5}{9}(F - 32).

Question 14

The perimeter of a triangle is 50 inches. The first side is 6 inches longer than the second side. The third side is twice the length of the second side. What is the length of the longest side?

  1. 11 inches
  2. 17 inches
  3. 22 inches (correct answer)
  4. 28 inches
Explanation: Let the length of the second side be xx. Then the first side is x+6x+6, and the third side is 2x2x. The perimeter is the sum of the sides: x+(x+6)+2x=50x + (x+6) + 2x = 50. Combine like terms: 4x+6=504x + 6 = 50. Subtract 6 from both sides: 4x=444x = 44. Divide by 4: x=11x = 11. This is the length of the second side. The lengths of the sides are: second side = 11 inches, first side = 11+6=1711+6=17 inches, and third side = 2(11)=222(11)=22 inches. The longest side is 22 inches.

Question 15

If 4x+13−2=x\frac{4x+1}{3} - 2 = x, what is the value of xx?

  1. -7
  2. -5
  3. -1
  4. 5 (correct answer)
Explanation: To solve this equation, first eliminate the fraction by multiplying every term by 3: 3(4x+13)−3(2)=3(x)3(\frac{4x+1}{3}) - 3(2) = 3(x). This simplifies to 4x+1−6=3x4x+1 - 6 = 3x. Combine the constant terms on the left: 4x−5=3x4x - 5 = 3x. To solve for xx, subtract 3x3x from both sides: x−5=0x - 5 = 0. Finally, add 5 to both sides: x=5x = 5.

Question 16

What is the value of yy that satisfies the equation 4(y−1)=2(2y+3)4(y - 1) = 2(2y + 3)?

  1. y=−2.5y = -2.5
  2. y=0y = 0
  3. There is no solution. (correct answer)
  4. The solution is all real numbers.
Explanation: Begin by distributing on both sides of the equation: 4y−4=4y+64y - 4 = 4y + 6. Next, attempt to isolate the variable yy. Subtract 4y4y from both sides: −4=6-4 = 6. This results in a statement that is false. A false statement like this indicates that there is no value of yy that can make the original equation true. Therefore, the equation has no solution.

Question 17

Half of a number increased by 10 is equal to five less than the number. What is the number?

  1. 15
  2. 20
  3. 30 (correct answer)
  4. 40
Explanation: Let the number be nn. Translating the sentence into a mathematical equation gives: 12n+10=n−5\frac{1}{2}n + 10 = n - 5. To solve for nn, first gather the nn terms on one side. Subtract 12n\frac{1}{2}n from both sides: 10=12n−510 = \frac{1}{2}n - 5. Next, add 5 to both sides: 15=12n15 = \frac{1}{2}n. Finally, multiply both sides by 2 to isolate nn: 30=n30 = n. The number is 30.

Question 18

A rental car company charges a flat fee of $45 plus $0.25 per mile driven. If the total charge for a rental was $132.50, how many miles were driven?

  1. 35 miles
  2. 350 miles (correct answer)
  3. 530 miles
  4. 710 miles
Explanation: Let mm be the number of miles driven. The total cost can be represented by the equation 45+0.25m=132.5045 + 0.25m = 132.50. To find the number of miles, first subtract the flat fee from the total charge: 0.25m=132.50−450.25m = 132.50 - 45, which simplifies to 0.25m=87.500.25m = 87.50. Then, divide by the per-mile charge: m=87.500.25m = \frac{87.50}{0.25}. This gives m=350m = 350. So, 350 miles were driven.

Question 19

If 7k−11=3k+57k - 11 = 3k + 5, what is the value of the expression 2k+12k + 1?

  1. -7
  2. 4
  3. 9 (correct answer)
  4. 12
Explanation: This is a two-step problem. First, solve the linear equation for kk. Subtract (3k) from both sides: 4k−11=54k - 11 = 5. Add 11 to both sides: 4k=164k = 16. Divide by 4: k=4k = 4. Second, substitute this value of kk into the expression 2k+12k + 1. This gives 2(4)+1=8+1=92(4) + 1 = 8 + 1 = 9. The value of the expression is 9.

Question 20

The sum of three consecutive odd integers is 141. What is the largest of these three integers?

  1. 45
  2. 47
  3. 49 (correct answer)
  4. 51
Explanation: Let the three consecutive odd integers be nn, n+2n + 2, and n+4n + 4. Their sum is n+(n+2)+(n+4)=141n + (n + 2) + (n + 4) = 141. Combine like terms: 3n+6=1413n + 6 = 141. Subtract 6 from both sides: 3n=1353n = 135. Divide by 3: n=45n = 45. This is the smallest of the three integers. The integers are 45, 47, and 49. The question asks for the largest integer, which is 49.