Solving an equation with parentheses

We come across problems about solutions of equations with parentheses.

In such cases, the parentheses are simplified by using the distributive property of multiplication over addition and subtraction. After simplification, the equations are solved as discussed in previous lesson by following the given rules in such cases.

Let us recall the distributive property of multiplication over addition and subtraction.

For any three numbers a, b, and c

1. a(b + c ) = ab + ac

2. a(b – c) = ab − ac

The example given below will make it easy to understand how to solve equations with parentheses.

Solve for w

7(w – 3) = 28

Solution

Step 1:

Given 7(w – 3) = 28

Using the distributive property of multiplication

7w – (7 × 3) = 28; 7w – 21 = 28

Step 2:

The variable to be solved for is w.

Adding 21 to both sides

7w – 21 + 21 = 28 + 21 = 49; 7w = 49

Step 3:

Dividing both sides by 7

$\frac{7w}{7} = \frac{49}{7}$

w = 7 is the solution

Step 4:

Checking the solution

Plugging in w = 7 in the original equation

7w – 21 = 28

7 × 7 – 21 = 28

49 – 21 = 28

28 = 28

So, the solution is verified to be correct.

Solve for w

4(z – 8) = 20

Solution

Step 1:

Given 4(z – 8) = 20

Dividing both sides of the equation by 4

$\frac{4(z – 8)}{4} = \frac{20}{4}$

z – 8 = 5

Step 2:

The variable to be solved for is z.

Adding 8 to both sides

z – 8 + 8 = 5 + 8 = 13

So, z = 13 is the solution

Step 3:

Checking the solution

Plugging in z = 13 in the original equation

4(z – 8) = 20

4(13 – 8) = 20

4(5) = 20

20 = 20

So, the solution is verified to be correct.