# INVERSE OPERATIONS

Inverse operations are opposite operations – one reverses the effect of the other.

• Addition and subtraction are inverse-operations
• Multiplication and division are inverse-operations  Inverse-operations are used to isolate the given variable.

## Solving equations using inverse operations examples

Example 1 :

Solve 7k = 35 using inverse operation

Solution :

Here 7 is multiplied by k. To find the value of k, we need to use inverse operation.

Inverse operation of multiplication is division

dividing by 7 on both sides, we get

7k/7 = 35/7

k = 5

Example 2 :

Solve k + 7 = 9 using inverse operation

Solution :

Here k is added to k. To find the value of k, we need to use inverse operation.

Inverse operation of addition is subtraction

Subtracting 7 on both sides, we get

k + 7 - 7 = 9 - 7

k = 2

Example 3 :

Solve b/8 = 7 using inverse operation

Solution :

Here b is divided by 8. To find the value of b, we need to use inverse operation.

Inverse operation of division is multiplication.

Multiplying by 8 on both sides, we get b = 56

Example 4 :

Solve m - 15 = 9 using inverse operation

Solution :

Here 15 is subtracted from m. To find the value of m, we need to use inverse operation.

Inverse operation of subtraction is addition.

Adding 15 on both sides, we get

m - 15 + 15  =  9 + 15

m  =  24

Example 5 :

Solve z + 17 = 23 using inverse operation

Solution :

Here 17 is added with z. To find the value of z, we need to use inverse operation.

Inverse operation of addition is subtraction.

Subtract 17 on both sides, we get

z + 17 - 17  =  23 - 17

z  =  6

Example 6 :

Solve 2 x + 5  = 23

Solution :

To find the value of x, we need to isolate x. Here 5 is added to 2x. In order to remove this 5, we have to subtract by 5 on both sides.

2 x + 5 - 5  =  23 - 5

2 x  =  18

Now x is multiplied by 2. To find the value of x we have to divide by 2 on both sides.

2x / 2 = 18 / 2

x = 9

Example 7 :

Solve p - 7  = 3

Solution :

Here 7 is subtracted from p. To isolate p we have to add by 7 on both sides.

Inverse operation of subtraction is addition.

p - 7 +  7 = 3 + 7

p = 10

Example 8 :

Solve 2r - 6 = 3

Solution :

Here 6 is subtracted from 2r. To isolate 2r, we have to add 6 on both sides.

2r - 6 + 6 = 3 + 6

2r = 9

2r/2 = 9/2

r = 9/2

Example 9 :

Solve 8 - p = 2

Solution :

Here p is subtracted from 8. To isolate p, we have to subtract 8 on both sides.

8 - p - 8  =  2 - 8

- p  =  -6

by multiplying -1 on both sides, we get

p  =  6

Example 10 :

Solve 10 - m = -15

Solution :

Here m is subtracted from 10. To isolate m, we have to subtract 10 on both sides.

10 - m - 10 = -15 - 10

- m  =  -25

by multiplying -1 on both sides, we get

m  =  25

## Related topics

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