SAT Math Quiz: Equations With One Variable

20 questions · exam conditions

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Equations With One VariableQuestion 1 of 20

A student rewrites a budget equation as $2.5x-7.5=0.5x+12.5$ . What is the value of $x$ ?

7.5

10

12.5

15

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SAT Math Quiz

SAT Math Quiz: Equations With One Variable

Practice Equations With One Variable in SAT 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 Equations With One Variable, giving you a quick way to practice the rules, question types, and explanations that matter most for SAT 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

A student rewrites a budget equation as $2.5x-7.5=0.5x+12.5$ . What is the value of $x$ ?

$7.5$
$10$ (correct answer)
$12.5$
$15$

Explanation: We need to solve

2.5x - 7.5 = 0.5x + 12.5

by first moving all x-terms to one side. Subtracting 0.5x from both sides gives

2x - 7.5 = 12.5

. Adding 7.5 to both sides yields

2x = 20

, so

x = 10

. A common mistake is making an arithmetic error when adding 7.5 + 12.5, perhaps getting 19 instead of 20, which would give

x = 9.5

. When working with decimals, take extra care with arithmetic and consider converting to fractions if that helps avoid errors.

Question 2

Solve for $x$ : $5(2x - 1) = 3(x + 7) + 4$ .

5
$\frac{7}{30}$
$\frac{25}{7}$
$\frac{30}{7}$ (correct answer)

Explanation: Distribute and combine to get

10x - 5 = 3x + 25

, so

7x = 30

and

x = \frac{30}{7}

. Other choices come from inverting the fraction, omitting the

+4

, or guessing

x=5

Question 3

Solve for $y$ in terms of $x$ if $3y - 4x = 9$ . What is $y$ ?

$y = \frac{9x + 4}{3}$
$y = \frac{9 - 4x}{3}$
$y = \frac{4x + 9}{3}$ (correct answer)
$y = \frac{4x - 9}{3}$

Explanation: This problem asks us to solve

3y - 4x = 9

for

y

in terms of

x

. To isolate

y

, first add

4x

to both sides:

3y = 9 + 4x

. Then divide both sides by

3

to get

y = \frac{4x + 9}{3}

. A common mistake is swapping the coefficient and constant term in the numerator, incorrectly writing

9x + 4

instead of

4x + 9

. When solving for one variable in terms of another, always perform the same operation to all terms on both sides of the equation.

Question 4

A gym charges a one-time sign-up fee plus a monthly cost. The total cost after $x$ months is modeled by $45+19x=12x+94$ . What is the value of $x$ , the number of months when the two cost plans are equal?

$7$ (correct answer)
$\dfrac{7}{49}$
$49$
$-7$

Explanation: This problem asks us to find when two gym cost plans are equal by solving the equation

45 + 19x = 12x + 94

. To solve, we first collect like terms by subtracting 12x from both sides:

45 + 19x - 12x = 94

, which gives us

45 + 7x = 94

. Next, we subtract 45 from both sides:

7x = 49

. Finally, we divide both sides by 7:

x = 7

. A common error is to incorrectly combine the x terms or make arithmetic mistakes when moving constants. When solving equations with variables on both sides, always move all variable terms to one side first.

Question 5

Solve the equation $7x - 5 = 3x + 19$ . What is the value of $x$ ?

$3.5$
$-3.5$
$6$ (correct answer)
$-6$

Explanation: To solve

7x - 5 = 3x + 19

, we need to isolate

x

by moving all variable terms to one side and constants to the other. Subtract

3x

from both sides:

7x - 3x - 5 = 19

, which gives us

4x - 5 = 19

. Add 5 to both sides:

4x = 24

. Divide by 4:

x = 6

. The common mistake is subtracting

3x

from the wrong side or making sign errors when moving constants. Always perform the same operation on both sides of the equation.

Question 6

To compare two phone plans, a student writes the equation $0.5x+7=0.2x+16$ , where $x$ is the number of gigabytes used in a month. What is the solution to the equation?

$10$
$30$ (correct answer)
$23$
$3$

Explanation: We need to solve

0.5x + 7 = 0.2x + 16

to find when the two phone plans cost the same. First, we collect like terms by subtracting

0.2x

from both sides:

0.5x - 0.2x + 7 = 16

, which simplifies to

0.3x + 7 = 16

. Next, subtract 7 from both sides:

0.3x = 9

. Finally, divide by 0.3:

x = 9 ÷ 0.3 = 30

. The plans are equal at 30 gigabytes. A common mistake is incorrectly combining the decimal coefficients. To avoid decimal division errors, you can multiply the entire equation by 10 first to work with whole numbers.

Question 7

Solve for $x$ : $\frac{3}{4}x - 5 = 1$ .

8 (correct answer)
3
-8
4

Explanation: Add 5 to get

\frac{3}{4}x = 6

, then multiply by

\frac{4}{3}

to find

x = 8

. The distractors come from adding or scaling incorrectly.

Question 8

A fundraiser's profit is modeled by $P=12n-35$ , where $P$ is profit in dollars and $n$ is the number of items sold. If the profit was $49$ dollars, what is the value of $n$ ?

$7$ (correct answer)
$6$
$9$
$10$

Explanation: Given

P = 12n - 35

and

P = 49

, we need to find the number of items sold

n

. Substituting:

49 = 12n - 35

. Add 35 to both sides:

49 + 35 = 12n

, which gives us

84 = 12n

. Divide both sides by 12:

n = 84 ÷ 12 = 7

. They sold 7 items to make a $49 profit. A common error is to subtract 35 from 49 instead of adding it when isolating the variable term. When the constant term is negative in the original equation, you add its absolute value to isolate the variable term.

Question 9

A phone plan's cost equation is $12 + 0.25x = 0.10x + 24$ , where $x$ is the number of texts. Solve for $x$ .

$80$ (correct answer)
$60$
$120$
$40$

Explanation: We need to solve

12 + 0.25x = 0.10x + 24

for the number of texts

x

. First, let's move all

x

terms to one side by subtracting

0.10x

from both sides:

12 + 0.25x - 0.10x = 24

, which gives us

12 + 0.15x = 24

. Subtract 12 from both sides:

0.15x = 12

. Divide by 0.15:

x = 12 ÷ 0.15 = 80

. The key error to avoid is making arithmetic mistakes when subtracting decimal coefficients. Double-check decimal operations to ensure accuracy.

Question 10

A formula for converting a measurement is given by $y=\frac{3}{4}x-5$ . Solve this equation for $x$ in terms of $y$ . Which expression correctly represents $x$ ?

$x=\frac{4}{3}(y+5)$ (correct answer)
$x=\frac{3}{4}(y+5)$
$x=\frac{4}{3}(y-5)$
$x=\frac{3}{4}(y-5)$

Explanation: We need to solve

y=\frac{3}{4}x-5

for

x

in terms of

y

. First, add 5 to both sides:

y + 5 = \frac{3}{4}x

. To isolate

x

, multiply both sides by the reciprocal of

\frac{3}{4}

, which is

\frac{4}{3}

\frac{4}{3}(y + 5) = \frac{4}{3} \cdot \frac{3}{4}x = x

. Therefore,

x = \frac{4}{3}(y + 5)

. A common mistake is incorrectly finding the reciprocal or forgetting to apply the operation to the entire expression

(y + 5)

. When solving for a variable, always perform the same operation on both sides of the equation.

Question 11

A fundraiser tracks money with the equation $4x+7=2x+31$ . What is the value of $x$ ? Since $x$ appears on both sides, subtract the smaller $x$ term from the larger one and then isolate $x$ by dividing correctly.

$19$
$12$ (correct answer)
$-12$
$-19$

Explanation: We need to solve

4x+7=2x+31

with variables on both sides. Subtract

2x

from both sides:

2x+7=31

. Subtract 7 from both sides:

2x=24

. Divide by 2:

x=12

. The key is to move all variable terms to one side and constants to the other by performing the same operation on both sides. Check your answer by substituting back:

4(12)+7=48+7=55

and

2(12)+31=24+31=55

✓.

Question 12

A student solves $\frac{3x}{4}-\frac{1}{2}=5$ to find a missing value in a data table. What is the value of $x$ ? Clear fractions carefully so you do not forget to multiply every term by the same number.

$6$
$\frac{22}{3}$ (correct answer)
$\frac{14}{3}$
$\frac{20}{3}$

Explanation: We need to solve

\frac{3x}{4}-\frac{1}{2}=5

. First, find a common denominator of 4:

\frac{3x}{4}-\frac{2}{4}=5

. Combine:

\frac{3x-2}{4}=5

. Multiply both sides by 4:

3x-2=20

. Add 2:

3x=22

. Divide by 3:

x=\frac{22}{3}

. The common error is forgetting to multiply all terms by the same number when clearing fractions. Always check that you've multiplied every term, including constants.

Question 13

Solve: $5(x - 2) = 3x + 4$ .

2
14
-3
7 (correct answer)

Explanation: Distribute and collect terms:

5x - 10 = 3x + 4 \Rightarrow 2x = 14 \Rightarrow x = 7

. The other choices reflect forgetting to divide by 2 (14), moving terms incorrectly (-3), or ignoring the constant 10 (2).

Question 14

Solve for $x$ in the equation $3x + 5 = 2x + 8$ . What is the value of $x$ ?

8
13
5
3 (correct answer)

Explanation: This problem asks us to solve the linear equation

3x + 5 = 2x + 8

for the value of

x

. First, subtract

2x

from both sides to get

3x - 2x + 5 = 8

, which simplifies to

x + 5 = 8

. Next, subtract

5

from both sides to isolate

x

x = 8 - 5 = 3

. A common error would be incorrectly combining like terms or making arithmetic mistakes when subtracting. To verify, substitute

x = 3

back into the original equation:

3(3) + 5 = 9 + 5 = 14

and

2(3) + 8 = 6 + 8 = 14

, confirming our solution is correct.

Question 15

A phone plan charges a $5$ monthly fee plus $0.10$ per text. If the total cost $C$ in dollars is given by $C = 0.10t + 5$ and last month the bill was $12.50$ , how many texts $t$ were sent?

80
70
65
75 (correct answer)

Explanation: Solve

0.10t + 5 = 12.50

to get

0.10t = 7.50

and

t = 75

Question 16

Seven more than four times a number equals 39. Which value of $x$ satisfies $4x + 7 = 39$ ?

6
7
9
8 (correct answer)

Explanation: Subtract 7 to get

4x = 32

, then divide by 4 to find

x = 8

Question 17

A formula for simple interest is $I = Prt$ . Solve this equation for $r$ in terms of $I$ , $P$ , and $t$ .

$r=\frac{IP}{t}$
$r=\frac{I}{Pt}$ (correct answer)
$r=\frac{Pt}{I}$
$r=\frac{It}{P}$

Explanation: We need to solve

I = Prt

for

r

. To isolate

r

, we need to divide both sides by everything that's multiplied with

r

, which is

P

and

t

. Dividing both sides by

Pt

\frac{I}{Pt} = \frac{Prt}{Pt} = r

. Therefore,

r = \frac{I}{Pt}

. The common mistake is dividing by only one of the factors (just

P

or just

t

) or incorrectly placing variables in the numerator when they should be in the denominator. When solving for a variable, divide by all factors multiplied with that variable.

Question 18

A formula for converting units is rearranged into $\frac{5}{9}(x-32)\=10$ . What is the value of $x$ ?

$50$ (correct answer)
$14$
$32$
$\frac{82}{5}$

Explanation: We need to solve

\frac{5}{9}(x - 32) \= 10

by isolating x. First, multiply both sides by

\frac{9}{5}

to clear the fraction:

x - 32 \= 10 \times \frac{9}{5} \= \frac{90}{5} \= 18

. Then add 32 to both sides to get

x \= 18 + 32 \= 50

. A common mistake is to multiply by

\frac{5}{9}

instead of its reciprocal

\frac{9}{5}

, which would give

x - 32 \= 10 \times \frac{5}{9} \= \frac{50}{9} \approx 5.56

, leading to

x \approx 37.56

. When a fraction multiplies a parenthetical expression, divide both sides by that fraction (multiply by its reciprocal) to isolate the parentheses.

Question 19

Adult tickets cost $x$ dollars each, and child tickets cost $(x - 4)$ dollars each. If 3 adult tickets and 2 child tickets total $44, what is $x$?

7.2
10.4 (correct answer)
8.8
9.6

Explanation: Write

3x + 2(x - 4) = 44 \Rightarrow 5x - 8 = 44

, so

x = 52/5 = 10.4

. Using

x

for both ticket types (8.8), treating children as

x + 4

(7.2), or misdistributing the 2 (9.6) are common errors.

Question 20

A gym charges a one-time registration fee plus a monthly fee. The total cost after 6 months is modeled by $18 + 6x = 96$ , where $x$ is the monthly fee in dollars. What is the value of $x$ ?

$12$
$13$ (correct answer)
$19$
$16$

Explanation: This problem asks us to find the monthly fee

x

when the total cost after 6 months is $96, given by the equation

18 + 6x = 96

. To solve, we first subtract 18 from both sides:

6x = 96 - 18 = 78

. Then we divide both sides by 6:

x = 78 ÷ 6 = 13

. The key error to avoid is dividing 96 by 6 before subtracting the registration fee of $18. When solving equations with multiple terms, always isolate the variable term by moving constants to the other side first.