Two-Step Equations Worksheet

32 printable problems that build from one-step to two-step and multi-step equations, plus word problems. The answer key shows the steps for every problem, not just the answer.

32 problems · answer key included · free, no sign-up

learnappu.com/math/algebra/two-step-equations-worksheet

Name ______________________Date __________ Period ____

Teachers and parents: print the student copy for class or homework, or print with the answer key on a separate page. You can also link to this page from your course site or LMS; no account is needed. Problems get harder within each section.

A. One-step equations

Solve. Undo the operation by doing the opposite to both sides.

1
$x + 7 = 15$
2
$y - 4 = - 9$
3
$6 n = 42$
4
$\frac{k}{3} = - 5$
5
$- 8 + m = 3$
6
$- 4 x = 28$
7
$\frac{t}{- 2} = 6$
8
$\frac{2}{3} x = 10$

B. Two-step equations

Solve. Undo addition or subtraction first, then multiplication or division.

9
$2 x + 5 = 17$
10
$3 x - 4 = 11$
11
$- 4 x + 9 = - 7$
12
$\frac{x}{3} + 2 = 8$
13
$5 - 2 x = 13$
14
$- \frac{x}{4} - 3 = 1$
15
$7 = 3 n - 8$
16
$\frac{2}{5} x + 1 = 9$
17
$\frac{x + 4}{3} = 5$
18
$0.2 x - 1.5 = 0.5$
19
$- 6 = 9 + 5 k$
20
$12 - \frac{x}{2} = 4$

C. Multi-step equations

Distribute and combine like terms first, get the variable on one side, then solve.

21
$3 (x - 2) = 15$
22
$2 x + 3 x - 4 = 21$
23
$5 x + 2 = 3 x + 10$
24
$4 (2 x + 1) - 3 x = 19$
25
$7 - 2 (x + 3) = - 9$
26
$6 x - (2 x - 5) = 29$
27
$\frac{x}{2} + \frac{x}{3} = 10$
28
$3 (2 x - 1) = 2 (x + 5) + 3$

D. Word problems

Write an equation, then solve it.

29
A gym charges a $25 sign-up fee plus $15 per month. You have paid $100 so far. How many months have you been a member?
30
Five more than twice a number is 31. What is the number?
31
A taxi charges $3 plus $2.50 per mile. The fare was $23. How many miles was the ride?
32
A rectangle has a perimeter of 50 cm. Its length is 7 cm more than its width. Find the width and length.

Answer key

Check your work after you finish each section.

A. One-step equations

1.
$x = 8$
Subtract 7 from both sides
2.
$y = - 5$
Add 4 to both sides
3.
$n = 7$
Divide both sides by 6
4.
$k = - 15$
Multiply both sides by 3
5.
$m = 11$
Add 8 to both sides
6.
$x = - 7$
Divide both sides by $- 4$
7.
$t = - 12$
Multiply both sides by $- 2$
8.
$x = 15$
Multiply both sides by $\frac{3}{2}$

B. Two-step equations

9.
$x = 6$
Subtract 5, then divide by 2
10.
$x = 5$
Add 4, then divide by 3
11.
$x = 4$
Subtract 9, then divide by $- 4$
12.
$x = 18$
Subtract 2, then multiply by 3
13.
$x = - 4$
Subtract 5, then divide by $- 2$
14.
$x = - 16$
Add 3, then multiply by $- 4$
15.
$n = 5$
Add 8, then divide by 3
16.
$x = 20$
Subtract 1, then multiply by $\frac{5}{2}$
17.
$x = 11$
Multiply by 3, then subtract 4
18.
$x = 10$
Add 1.5, then divide by 0.2
19.
$k = - 3$
Subtract 9, then divide by 5
20.
$x = 16$
Subtract 12, then multiply by $- 2$

C. Multi-step equations

21.
$x = 7$
Distribute: $3 x - 6 = 15$
22.
$x = 5$
Combine like terms: $5 x - 4 = 21$
23.
$x = 4$
Variables to one side: $2 x = 8$
24.
$x = 3$
Distribute and combine: $5 x + 4 = 19$
25.
$x = 5$
Distribute: $1 - 2 x = - 9$
26.
$x = 6$
Distribute the minus: $4 x + 5 = 29$
27.
$x = 12$
Multiply every term by 6: $3 x + 2 x = 60$
28.
$x = 4$
Distribute both sides: $6 x - 3 = 2 x + 13$

D. Word problems

29.
$5$ months
Equation: $25 + 15 m = 100$
30.
$13$
Equation: $2 n + 5 = 31$
31.
$8$ miles
Equation: $3 + 2.5 d = 23$
32.
Width $9$ cm, length $16$ cm
Equation: $2 w + 2 (w + 7) = 50$

How to solve two-step equations

A two-step equation has the variable multiplied (or divided) by a number and a number added (or subtracted), like $3 x - 4 = 11$ . Solve it by undoing those operations in reverse order.

Step 1: undo the addition or subtraction. Add 4 to both sides: $3 x = 15$ .

Step 2: undo the multiplication or division. Divide both sides by 3: $x = 5$ .

Check: $3 (5) - 4 = 11$ . True, so $x = 5$ is correct.

Fractions: for $\frac{x}{3} + 2 = 8$ , subtract 2 and then multiply by 3. For $\frac{2}{5} x + 1 = 9$ , subtract 1 and then multiply by the reciprocal, $\frac{5}{2}$ .

Common mistake: dividing only part of an equation. If you divide first in $2 x + 5 = 17$ , you must divide every term: $x + 2.5 = 8.5$ . Subtracting first avoids decimals and fractions.

Read the full Linear Equations lesson with worked examples →

Frequently asked questions

How do you solve a two-step equation?

Undo the operations in reverse order. First add or subtract to get the variable term alone, then multiply or divide to get the variable alone. For 2x + 5 = 17: subtract 5 from both sides to get 2x = 12, then divide both sides by 2 to get x = 6.

What is the difference between one-step, two-step and multi-step equations?

A one-step equation needs one inverse operation (x + 7 = 15). A two-step equation needs two (2x + 5 = 17). A multi-step equation needs more, usually distributing, combining like terms or moving variables from both sides before the final two steps.

What do I do when the variable is on both sides?

Add or subtract to move all the variable terms to one side and all the numbers to the other. For 5x + 2 = 3x + 10, subtract 3x from both sides to get 2x + 2 = 10, then solve the two-step equation: x = 4.

How do I check my answer?

Substitute it into the original equation. If both sides are equal, it is correct. For x = 6 in 2x + 5 = 17: 2(6) + 5 = 17. True.

What grade are two-step equations?

Two-step equations are typically taught in 7th grade (Common Core 7.EE.B.4) and reviewed in 8th grade and Algebra 1, where multi-step equations and variables on both sides are added.

Stuck on a problem?

LearnAppu's AI tutor walks you through the exact step you missed, then gives you more practice like it. Lesson 1 is free.

Practice with the AI tutor free

More free worksheets and lessons

Linear Equations lessonForms of a linear equation and how to solve them Systems of Equations Worksheet23 problems with an answer key Algebra 1 courseEvery Algebra 1 unit with practice and an AI tutor