Multiplicative property of equality

Definition

The multiplicative property of equality states that we can multiply ordivide both sides of an equation by the same nonzero number oralgebraicexpression without changing the solution.

If a, b and c are any three numbers

If a = b, and c 0, then

1. a × c = b × c

2. a ÷ c = b ÷ c

Example 1

Solve for x

2x = 3.58

Solution

Step 1:

To solve for x, we must isolate x. On left side of equation, we have 2x; to isolate x, we must divide by 2.

Step 2:

From the multiplicative property of equality with decimals we must divide both sides of an equation by the same number. So, we divide the both sides by 2 to get

2xx=3.582

Step 3:

Simplifying

3.582=1.79

So, the solution is x = 1.79

Example 2

Solve for x

x3=4.27

Solution

Step 1:

To solve for x, we must isolate x. On left side of equation, we have x3; to isolate x, we must multiply by 3.

Step 2:

From the multiplicative property of equality with decimals we must multiply both sides of an equation by the same number. So, we multiply both sides by 3 to get

x3×3=4.27×3

Step 3:

Simplifying

4.27 × 3 = 1281

So, the solution is x = 12.81