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Two-step equations and inequalities - Printable Mathematics Worksheets - Wayground

Two-step equations and inequalities

24 questions

6th - 6th Grade

Mathematics

Two-step equations and inequalities is a Grade 6 mathematics worksheet with 24 multiple-choice questions that helps students solve for an unknown variable. The items require students to use inverse operations, isolate the variable, and select solutions that may include positive numbers, negative numbers, and fractions or decimals. Several questions use forms such as a variable multiplied by a coefficient and combined with a constant, while others ask students to identify the purpose of solving an equation. This free printable worksheet gives students focused practice recognizing the goal of solving an equation and evaluating their solutions against multiple-choice options. It is useful for introducing or reviewing two-step equations and inequalities, checking individual understanding, assigning independent practice, or preparing for an assessment. A complete answer key is included so teachers can review results efficiently and address errors in signs, operations, or division by the coefficient.

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Worksheets

Two-step equations and inequalities

Total questions: 24

Name
Class
Date
1.

7k - 14 = 42

a)

7

b)

-8

c)

0

d)

8

2.

3g - 5 =17

a)

10

b)

-7

c)

7.33333333333

d)

6

3.

9=4g+13

a)

1

b)

-1

c)

0

d)

3

4.

13= 5m -2

a)

-3

b)

2

c)

3

d)

-2

5.

Solve the equation for m.

−15=−4m+5-15=-4m+5  

a)

4

b)

7

c)

5

d)

2.5

6.

Solve for x.

x+93=−2\frac{x+9}{3}=-2

a)

-15

b)

-3

c)

15

d)

-8

7.
When solving an equation, our goal is to:
a)
bake cookies.
b)
use a calculator.
c)
eat lunch.
d)
find the unknown value.
8.
11b+7=40
a)
2
b)
1
c)
4
d)
3
9.
Solve  9 + 3x = 10
a)
2/3
b)
1/3
c)
-1/3
d)
4
10.
3c + 5 = 23
a)
c = 3
b)
c = 6
c)
c = 7
d)
c = 18
11.
4x + 7 = 23
a)
x = 16
b)
x = 4
c)
x = 9
d)
x = 12
12.
Figure out what n equals in this equation:
6n + 4 = -26
a)
n=-6
b)
n= -5
c)
n= 8
d)
n= -4
13.
    2x + 6 = 14
a)
x = 4
b)
x = 10
c)
x = -4
d)
x = 3
14.
6p - 5 =13
a)
12
b)
15
c)
3
d)
-3
15.

Find the solution

a)

X≥4X\ge4

b)

X≤4X\le4

c)

X ≤ 10X\ \le\ 10

d)

X > 4X\ >\ 4

16.

Find the solution

a)

X ≥ 4X\ \ge\ 4

b)

X≤4X\le4

c)

X < 4X\ <\ 4

d)

X > 4X\ >\ 4

17.

Which number line matches X ≥ 4X\ \ge\ 4  ?

a)
b)
c)
d)
18.

Which number line matches X ≤ 4X\ \le\ 4  

a)
b)
c)
19.
16 - 4a > 8
a)
a<-2
b)
a>-2
c)
a<2
d)
a>2
20.
Do I need to flip my sign?
-3x  ≥ 12
a)
Yes
b)
No
21.
When graphing b < 6 would you use an open or closed circle?
a)
Open
b)
closed
22.
Solve and graph the inequality.
7n - 1 > 76
a)
A
b)
B
c)
C
d)
D
23.
25 < X - 10
a)
X > 35
b)
X < 35
c)
X > -35
d)
X < -35
24.
Solve 8 + 4x > 24
a)
x > 4
b)
x > 8
c)
x > 64
d)
x < 8
Answer Key

Two-step equations and inequalities

Total questions: 24

1.
d)

8

2.
c)

7.33333333333

3.
b)

-1

4.
c)

3

5.
c)

5

6.
a)

-15

7.
d) find the unknown value.
8.
d) 3
9.
b) 1/3
10.
b) c = 6
11.
b) x = 4
12.
b) n= -5
13.
a) x = 4
14.
c) 3
15.
a)

X≥4X\ge4

16.
b)

X≤4X\le4

17.
a)
18.
c)
19.
c) a<2
20.
a) Yes
21.
a) Open
22.
c) C
23.
a) X > 35
24.
a) x > 4

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FAQs

What does this worksheet cover?

This Grade 6 worksheet covers solving two-step equations and inequalities with 24 multiple-choice questions. Students isolate the unknown using inverse operations and choose solutions that include positive values, negative values, fractions, and decimals.

How can I use this worksheet to teach two-step equations and inequalities?

Model a two-step example by undoing the constant operation first and then dividing by the coefficient, while explaining that each operation must preserve the equation's balance. Have students apply the same sequence to the multiple-choice items, then ask them to substitute a selected value back into an equation to verify it. Use the questions involving negative or fractional solutions to discuss why a solution does not need to be a whole number.

What mistakes should I watch for when students complete this worksheet?

Students may undo the multiplication before removing the added or subtracted constant, apply an inverse operation incorrectly, or divide the constant by the wrong coefficient. Watch especially for sign errors in items with negative constants or solutions and for selecting a whole-number distractor when the correct answer is a fraction or decimal. Because the worksheet is multiple choice, ask students to show their steps rather than choosing an answer by estimation alone.

How do I assign and grade this worksheet?

On Wayground, assign it as a printable PDF or as a digital quiz, and use the complete answer key to check the 24 multiple-choice responses. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time.

How can I differentiate this worksheet for my students?

In the worksheet's Advanced Settings, adjust font spacing or choose a larger font size to make the multiple-choice equations and answer options easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the two-step equation and inequality practice intact.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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