Inverse operations are opposite operations. That is, one reverses the effect of the other.

- Addition and subtraction are inverse operations
- Multiplication and division are inverse operations

In solving problems in algebra, we use inverse operations to isolate the given variable.

**Example 1 :**

Solve for k :

7k = 35

**Solution :**

Here 7 and k are multiplied.

So, we have to use the inverse operation of multiplication to solve for k.

Inverse operation of multiplication is division.

7k = 35

Divide both sides by 7.

k = 5

**Example 2 :**

Solve for k ;

k + 7 = 9

**Solution :**

Here 7 is added to k.

So, we have to use the inverse operation of addition to solve for k.

Inverse operation of addition is subtraction.

k + 7 = 9

Subtract 7 from each side.

k = 2

**Example 3 :**

Solve for b :

b/8 = 7

**Solution :**

Here b is divided by 8.

So, we have to use the inverse operation of division to solve for b.

Inverse operation of division is multiplication.

b/8 = 7

Multiply each side by 8.

b = 56

**Example 4 :**

Solve for m :

m - 15 = 9

**Solution :**

Here 15 is subtracted from m.

So, we have to use the inverse operation of subtraction to solve for b.

Inverse operation of subtraction is addition.

m - 15 = 9

Add 15 to each side.

m = 24

**Example 5 :**

Solve for z :

z + 17 = 23

**Solution :**

Here 17 is added with z.

So, we have to use the inverse operation of addition to solve for k.

Inverse operation of addition is subtraction.

z + 17 = 23

Subtract 17 from each side.

z = 6

**Example 6 :**

Solve for x :

2x + 5 = 23

**Solution :**

Here 5 is added to 2x.

So, we have to use the inverse operation of addition to solve for 2x.

Inverse operation of addition is subtraction.

2x + 5 = 23

Subtract 5 from each side.

2x = 18

Here 2 and x are multiplied.

Then, we have to use the inverse operation of multiplication to solve for x.

Inverse operation of multiplication is division.

2x = 18

Divide each side by 2.

x = 9

**Example 7 :**

Solve for p :

2p - 7 = 3

**Solution :**

Here 7 is subtracted from p.

So, we have to use the inverse operation of subtraction to solve for 2x.

Inverse operation of subtraction is addition.

2p - 7 = 3

Add 7 to each side.

2p = 10

Here 2 and p are multiplied.

Then, we have to use the inverse operation of multiplication to solve for x.

Inverse operation of multiplication is division.

2p = 10

Divide each side by 2.

p = 5

**Example 8 :**

Solve for r :

(r - 6)/2 = 3

**Solution :**

Here (r - 6) is divided by 2.

So, we have to use the inverse operation of division to solve for (r - 6).

Inverse operation of division is multiplication.

(r - 6)/2 = 3

Multiply each side by 2.

r - 6 = 6

Here 6 is subtracted from r.

Then, we have to use the inverse operation of subtraction to solve for r.

Inverse operation of subtraction is addition.

r - 6 = 6

Add 6 to each side.

r = 12

**Example 9 :**

Solve for p :

(p/3) - 4 = 0

**Solution :**

Here 4 is subtracted from (p/3).

So, we have to use the inverse operation of subtraction to solve for (p/3).

Inverse operation of subtraction is addition.

(p/3) - 4 = 0

Add 4 to each side.

p/3 = 4

Here p is divided by 3.

Then, we have to use the inverse operation of division to solve for p.

Inverse operation of division is multiplication.

p/3 = 4

Multiply each side by 3.

p = 12

**Example 10 :**

Solve for m :

10 - 3m = -5

**Solution :**

10 - 3m = -5

Add 3m to each side.

10 = -5 + 3m

Add 5 to each side.

15 = 3m

Divide each side by 3.

5 = m

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