Linear equations worksheet with answers :

Here we are going to see some practice questions on the topic solving linear equations with one variable.

You can find detailed solution for each questions.

Linear equations worksheet with answers - Questions

(1) Solve 6r + 7 = 13 + 7r

(2) Solve 13 - 4x = 1 - x

(3) Solve  −7x − 3x + 2 = −8x − 8

(4) Solve  −7x − 3x + 2 = −8x − 8

(5) Solve  −14 + 6b + 7 − 2b = 1 + 5b

(6) Solve -6x - 20 = -2x + 4(1-3x)

(7)  Solve 4n − 40 = 7(−2n + 2)

(8) Solve −31 − 4x = −5 − 5(1 + 5x)

(9)  Solve 4(−8x + 5) = −32x − 26

(10) Solve −3(x − 1) + 8(x − 3) = 6x + 7 − 5x

Linear equations worksheet with answers - Solutions

Problem 1 :

Solve 6r + 7 = 13 + 7r

Solution :

6r + 7 = 13 + 7r

Subtract 7r on both sides

6r - 7r + 7 = 13 - 7r

-1r + 7 = 13

Subtract 7 on both sides

-1r + 7 - 7 = 13 - 7 ==> -r = 6 ==> r = - 6

Hence the value of r is -6.

Problem 2 :

Solve 13 - 4x = 1 - x

Solution :

13 - 4x = 1 - x

13 - 4x + x = 1 - x + x

13 - 3x = 1

Subtract 13 on both sides

13 - 13 - 3x = 1 - 13

-3x = -12

Divide by -3 on both sides

x = 4

Hence the value of x is 4.

Problem 3 :

Solve  −7x − 3x + 2 = −8x − 8

Solution :

−7x − 3x + 2 = −8x − 8

First we have to combine the x terms in the left hand side.

−10x + 2 = −8x − 8

Now add 8x on both sides

-10x + 8x + 2 = -8x + 8x - 8

-2x + 2 = -8

Subtract 2 on both sides

-2x + 2 - 2 = -8 - 2

-2x = -10

Divide by -2 on both sides

x = 5

Hence the value of x is 5.  Linear equations worksheet with answers

Problem 4 :

Solve   −7x − 3x + 2 = −8x − 8

Solution :

−7x − 3x + 2 = −8x − 8

First we have to combine the x terms in the left hand side.

−10x + 2 = −8x − 8

Now add 8x on both sides

-10x + 8x + 2 = -8x + 8x - 8

-2x + 2 = -8

Subtract 2 on both sides

-2x + 2 - 2 = -8 - 2

-2x = -10

Divide by -2 on both sides

x = 5

Hence the value of x is 5.

Problem 5 :

Solve  −14 + 6b + 7 − 2b = 1 + 5b

Solution :

−14 + 6b + 7 − 2b = 1 + 5b

First we have to combine b terms and constants in the left hand side.

−7 + 4b = 1 + 5b

Subtract by 5b on both sides

-7 + 4b - 5b = 1 + 5b - 5b

-b - 7 = 1

Subtract 7 on both sides

-b - 7 + 7 = 1 + 7

-b = 8 ==> b = -8

Hence the value of b is -8.

Problem 6 :

Solve  -6x - 20 = -2x + 4(1-3x)

Solution :

-6x - 20 = -2x + 4(1-3x)

Distribute 4

-6x - 20 = -2x + 4 - 12x

-6x - 20 = -14x + 4

-6x + 14x -20 = -14x + 4 + 14x

8x - 20 = 4

8x - 20 + 20 = 4 + 20

8x = 24

Divide by 8 on both sides

x = 3

Hence the value of x is 3.

Problem 7 :

Solve 4n − 40 = 7(−2n + 2)

Solution :

4n − 40 = 7(−2n + 2)

Distribute 7

4n − 40 = -14n + 14

4n + 14n − 40 = -14n + 14n + 14

18n - 40 = 14

18n - 40 + 40 = 14 + 40

18n = 54

Divide by 18 on both sides

n = 3

Hence the value of n is 3.

Problem 8 :

Solve  −31 − 4x = −5 − 5(1 + 5x)

Solution :

−31 − 4x = −5 − 5(1 + 5x)

Distribute -5

−31 − 4x = −5 − 5 - 25x

−31 − 4x = −10 - 25x

-31 - 4x + 25x = -10 - 25x + 25x

-31 + 21x = -10

-31 + 31 + 21x = -10 + 31

21x = 21

Divide by 21 on both sides

x = 1

Hence the value of x is 1.

Problem 9 :

Solve  4(−8x + 5) = −32x − 26

Solution :

4(−8x + 5) = −32x − 26

Distribute 4

-32x + 20 = −32x − 26

-32x + 32x + 20 = -32x + 32x - 26

Since both side x terms are going to canceled.

Hence there is no solution for x.

Problem 10 :

Solve   −3(x − 1) + 8(x − 3) = 6x + 7 − 5x

Solution :

−3(x − 1) + 8(x − 3) = 6x + 7 − 5x

Distribute -3 and 8

−3x + 3 + 8x − 24 = 6x + 7 − 5x

5x - 21 = 1x + 7

Subtract 1x on both sides

5x - 1x - 21 = 1x - 1x + 7

4x - 21 = 7

4x - 21 + 21 = 7 + 21

4x = 28

Divide by 4 on both sides

x = 7

Hence the value of x is 7.

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