7th Grade Solving Two-Step Equations Worksheet Solutions (PDF)

7th Grade math worksheet solutions: Solving Two-Step Equations – Maths PDF

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This two step equations answers for 7th Grade covers solving two-step equations (Common Core 7.EE.B.4a), with a free PDF to print.

Use this answer key to check your work on the two-step equations worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

Grade 7 · Common Core State Standards: 7.EE.B.4a

Two step equations answers: exercises 1 to 10

Exercise 1 – Add then divide

Subtract $5$ from both sides: $2x=12$

Divide both sides by $2$: $x=6$

Check: $2(6)+5=17$

$x=6$

x = 6.

Exercise 2 – Subtract then divide

Add $4$ to both sides: $3x=18$

Divide both sides by $3$: $x=6$

Check: $3(6)-4=14$

$x=6$

Exercise 3 – Divide by a number

Subtract 3 from both sides: $\frac{x}{4}=5$.

Multiply both sides by 4: $x=20$.

Check: $\frac{20}{4}+3=8$

$x=20$

Exercise 4 – Negative coefficient

Subtract $2$ from both sides: $-5x=-20$

Divide both sides by $-5$: $x=4$

Check: $-5(4)+2=-18$

$x=4$

Exercise 5 – Distribute first or divide first

Divide both sides by $4$: $x+3=8$

Subtract $3$ from both sides: $x=5$

Check: $4(5+3)=32$

$x=5$

Each group is 8.

Exercise 6 – Negative solution

Divide both sides by $3$: $x-2=-5$

Add $2$ to both sides: $x=-3$

Check: $3(-3-2)=-15$

$x=-3$

Exercise 7 – Decimals

Subtract $1.2$ from both sides: $0.5x=3.5$

Divide both sides by $0.5$: $x=7$

Check: $0.5(7)+1.2=4.7$

$x=7$

Solution steps.

Exercise 8 – Fractions

Add $\frac{3}{4}$ to both sides: $\frac{1}{2}x=2$

Divide both sides by $\frac{1}{2}$: $x=4$

Check: $\frac{1}{2}(4)-\frac{3}{4}=\frac{5}{4}$

$x=4$

Exercise 9 – Decimals in parentheses

Divide both sides by $-2$: $x+1.5=4.5$

Subtract $1.5$ from both sides: $x=3$

Check: $-2(3+1.5)=-9$

$x=3$

Exercise 10 – Negative divisor

Subtract 4: $\frac{x}{-3}=6$.

Multiply both sides by $-3$: $x=-18$.

Check: $\frac{-18}{-3}+4=6+4=10$

$x=-18$

Exercises 11 and up

Exercise 11 – Fraction coefficient

Subtract $4$ from both sides: $\frac{2}{3}x=6$

Divide both sides by $\frac{2}{3}$: $x=9$

Check: $\frac{2}{3}(9)+4=10$

$x=9$

Exercise 12 – Variable term first

Subtract $7$ from both sides: $-2x=-6$

Divide both sides by $-2$: $x=3$

Check: $-2(3)+7=1$

$x=3$

Exercise 13 – Decimal coefficient

Subtract $4.5$ from both sides: $0.3x=1.8$

Divide both sides by $0.3$: $x=6$

Check: $0.3(6)+4.5=6.3$

$x=6$

Exercise 14 – Fraction in parentheses

Divide both sides by $6$: $x+\frac{1}{2}=\frac{5}{2}$

Subtract $\frac{1}{2}$ from both sides: $x=2$

Check: $6(2+\frac{1}{2})=15$

$x=2$

Exercise 15 – Phone bill

Equation: $0.05m+20=32.50$.

Subtract 20: $0.05m=12.50$.

Divide by 0.05: $m=250$.

250 minutes

Exercise 16 – Gym membership

$12m+15=99$.

$12m=84$.

$m=7$

7 months

Exercise 17 – Perimeter

Divide by 2: $12+w=20$.

Subtract 12: $w=8$.

8 feet

Exercise 18 – Falling temperature

$8-3h=-10$.

Subtract 8: $-3h=-18$.

Divide by $-3$: $h=6$

6 hours

Exercise 19 – Arithmetic and algebra

(a) Take off the fee: $53-5=48$. Then share: $48\div 4=12$.

(b) $4t+5=53$, so $4t=48$ and $t=12$.

$12 per ticket

Exercise 20 – Saving up

$4.5w+2.75=29.75$.

$4.5w=27$.

$w=6$

6 weeks

Savings over time.

Exercise 21 – Number puzzle

$3n-7.5=12$.

Add 7.5: $3n=19.5$.

$n=6.5$

6.5

Key facts behind this two step equations answers

Key facts

Two forms: $px + q = r$ and $p(x + q) = r$.
Undo addition or subtraction first, then multiplication or division.
Do the same operation to both sides.
Fractions and decimals follow the same steps as whole numbers.
Check by substituting the solution into the original equation.

How to use this two step equations answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the two step equations answers as a PDF with the button below and keep it with your notes.

All Grade 7 chapters: Grade 7 math.

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