**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.

(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

**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

Add x on both sides

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

Add 14x on both sides

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

8x - 20 = 4

Add 20 on both sides

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

Add 14n on both sides

4n + 14n − 40 = -14n + 14n + 14

18n - 40 = 14

Add 40 on both sides

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

Add 25x on both sides

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

-31 + 21x = -10

Add 31 on both sides

-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

Add 32x on both sides

-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

Add 21 on both sides

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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