Linear Equations – Inverse Method

Solve the following equations and check answers:

1. x + 4 = 9

Solution: Given x + 4 = 9

Subtracting 4 to both sides we get,

x + 4 – 4 = 9 – 4

x = 5

Check: Substituting x = 5 in LHS, we get,

LHS = x + 4

= 5 + 4

= 9

RHS = 9

LHS = RHS

Hence, Checked.

2. x – 2 = 8

Solution: Given x – 2 = 8

Adding 2 to both sides we get,

x – 2 + 2 = 8 + 2

x = 10

Check: Substituting x = 10 in LHS, we get,

LHS = x – 2 = 10 – 2 = 8

RHS = 8

LHS = RHS

Hence, Checked.

3. x + 8 = 13

Solution: Given x + 8 = 13

Subtracting 8 to both sides we get,

x + 8 – 8 = 13 – 8

x = 5

Check: Substituting x = 5 in LHS, we get,

LHS = x + 8 = 5 + 8 = 13

RHS = 13

LHS = RHS

Hence, Checked.

4. x + (5/4) = 9/4

Solution: Given x + (5/4) = (9/4)

Subtracting (5/4) to both sides we get,

x + (5/4) – (5/4) = (9/4) – (5/4)

x = (4/4)

Check: Substituting x = (4/4) in LHS, we get,

LHS = x + (5/4) = (4/4) + (5/4) = (9/4)

RHS = (9/4)

LHS = RHS

Hence, Checked.

5. 5x = 35

Solution: Given 5x = 35

Dividing both sides by 5 we get,

(5x/5) = 35/5

x = 7

Check: Substituting x = 7 in LHS, we get,

LHS = 5x = 5 x 7 = 35

RHS = 35

Therefore, LHS = RHS

Hence, Checked.

6. 11x = 66

Solution: Given 11x = 66

Dividing both sides by 11

we get, (11x/11) = 66/11

x = 6

Check: Substituting x = 6 in LHS, we get,

LHS = 11 x 6 = 66

RHS = 66

Therefore, LHS = RHS

Hence, Checked.

7. 8x = 0

Solution: Given 8x = 0

Dividting both sides by 8 we get,

(8x/8) = (0/8)

x = 0

Check: Substituting x = 0 in LHS, we get,

LHS = 8x = 8 x 0 = 0

RHS = 0

Therefore, LHS = RHS

Hence, Checked.

8. (x/3) = 0

Solution: Given (x/3) = 0

Multiplying both sides by 3 we get,

(x/3) x 3 = 0 x 3 = 0

x = 0

Check: Substituting x = 0 in LHS, we get,

LHS = 0/3 = 0

RHS = 0

Therefore, LHS = RHS

Hence, Checked.

9. x – (1/4) = (3/4)

Solution: Given x – (1/4) = (3/4)

Adding (1/4) both sides we get,

x – (1/4) + (1/4) = (3/4) + (1/4)

x = 4/4

Check: Substituting x = 4/4 in LHS, we get,

LHS = (4/4) – (1/4) = (3/4)

RHS = (3/4)

Therefore, LHS = RHS = (3/4)

Hence, Checked.

10. x + (2/5) = (6/5)

Solution: Given x + (2/5) = (6/5)

Subtracting (2/5) from both sides we get,

x + (2/5) – (2/5) = (6/5) – (2/5)

x = (4/5)

Check: Substituting x = 4/5 in LHS, we get,

LHS = (4/5) + (2/5) = (6/5)

RHS = (6/5)

Therefore, LHS = RHS = (6/5)

Hence, Checked.

11. 9 – x = 4

Solution: Given 9 – x = 4

Subtracting 9 from both sides we get,

9 – x – 9 = 4 – 9

x = -5

Multiplying both sides by -1, we get

(-x) x (-1) = (-5) x (-1)

x = 5

Check: Substituting x = 5 in LHS, we get,

LHS = 9 – x = 9 – 5 = 4

RHS = 4

Therefore, LHS = RHS

Hence, Checked.

12. 5 + 7x = -30

Solution: Given 5 + 7x = -30

Subtracting 5 from both sides we get,

5 + 7x – 5 = -30 – 5

7x = -35

x = (-35/7)

x = -5

Check: Substituting x = -5 in LHS, we get,

LHS = 5 + 7x = 5 + 7 x (-5)

= 5 – 35 = -30

RHS = -30

LHS = RHS

Hence, Checked.

13. (6/5) – x = (2/5)

Solution: Given (6/5) – x = (2/5)

Subtracting (6/5) from both sides we get,

(6/5) – x – (6/5) = (2/5) – (6/5)

-x = -(4/5)

x = 4/5

Check: Substituting x = (4/5) in LHS, we get,

LHS = (6/5) – (4/5) = (2/5)

RHS = (2/5)

Therefore, LHS = RHS = (2/5)

Hence, Checked.

14. x – (8/3) = (5/3)

Solution: Given x – (8/3) = (5/3)

adding (8/3) both sides we get,

x – (8/3) + (8/3) = (5/3) + (8/3)

x = [(8 + 5)/3]

x = 11/3

Check: Substituting x = (11/3) in LHS, we get,

LHS = (11/3) – (8/3) = (5/3)

RHS = (5/3)

Therefore, LHS = RHS = (5/3)

Hence, Checked.

15. 2x – (1/2) = (-1/3)

Solution: Given 2x – (1/2) = (-1/3)

Adding (1/2) from both sides we get,

2x + (1/2) – (1/2) = (-1/3) + (1/2)

x = (-2 + 3)/6 [6 is LCM of 3 and 2]

2x = 1/6

Divide both sides by 2, we get

2x/2 = (1/6×2)

x = 1/12

Check: Substituting x = (1/12) in

LHS, we get,

LHS = (2 x 1/12) – (1/2)

= (1/6) – (1/2)

= (1 – 3)/6 = – 2/6 = -1/3

RHS = (-1/3)

Therefore, LHS = RHS = (-1/3)

Hence, Checked.

16. 5(x + 3) = 25

Solution: Given 5 (x + 3) = 25

deviding both sides by 5 we get,

[5 (x + 3)]/5 = 25/5

(x + 3) = 5

Subtracting both sides by 3 we get,

x + 10 – 3 = 5 – 3

x = 2

Check: Substituting x = 2 in LHS, we get,

LHS = 5 (2 + 3) = 5 x 5 = 25

RHS = 25

Therefore, LHS = RHS = 25

Hence, Checked.

17. 12 = (6x/10) – 9

Solution: Given 12 = (6x/10) – 9

Adding 9 to both sides we get,

12 + 9 = (6x/10) – 9 + 9

21 = (6x/10)

Multiply both sides by 10 we get,

21 x 10 = [(6x) x 10]/10

210 = 6x

Divide both sides by 6, we get

210/6 = 6x/6

35 = x

x = 35

Check: Substituting x = 35 in RHS

we get, [(6 x 35)/10] – 9

RHS = (210/10 – 9)

= (21- 9) = 12

LHS = 12

Therefore, LHS = RHS = 12

Hence, Checked.

18. (x + 10) = 80

Solution: Given 4 (x + 10) = 80

dividing 4 by both sides we get,

[4 (x + 10)]/4 = 80/4

(x + 10) = 20

Subtracting both sides by 10 we get,

x + 10 – 10 = 20 – 10

x = 10

Check: Substituting x = 10 in LHS, we get,

LHS = 4 (10 + 10) = 4 x 20 = 80

RHS = 80

Therefore, LHS = RHS = 80

Hence, Checked.

19. 5(x + 3) = 25

Solution: Given 5 (x + 3) = 25

dividing both sides by 5 we get,

[5 (x + 3)]/5 = 25/5

(x + 3) = 5

Subtracting both sides by 3 we get,

x + 10 – 3 = 5 – 3

x = 2

Check: Substituting x = 2 in LHS, we get,

LHS = 5 (2 + 3) = 5 x 5 = 25

RHS = 25

Therefore, LHS = RHS = 25

Hence, Checked.

20. (x/2) = (5/4)

Given: (x/2) = (5/4)

Multiply both sides by 2 we get,

(x/2) x 2 = (5/4) x 2

x = 5/8

Check: Substituting x = 5/8 in LHS, we get,

LHS = (x/2) = (5/8)/2 = 5/4

RHS = 5/4

Therefore, LHS = RHS = 5/4

Hence, Checked.

21. 3(x + 3) + 2 (x + 4) = 12

Solution: Given 3 (x + 3) + 2(x + 4) = 25

simplifying the brackets, we get,

3x + 9 + 2x + 8 = 12

3x + 2x + 9 + 8 = 12

5x + 17 = 12

Subtracting both sides by 12 we get,

5x + 17 – 12 = 12 – 12

5x + 5 = 0

5x = -5

x = -5/5

x= -1

Check: Substituting x = -1 in LHS, we get,

LHS = [3 x (-1 + 3)] + 2 [(-1 + 4)]

= [-3 + 9] + [-2 + 8] = 6 + 6 = 12

RHS = 12

Therefore, LHS = RHS = 12

Hence, Checked.