Additive property of equality with decimals

Definition

The additive property of equality states that we can add orsubtract the same number oralgebraicexpression to both sides of an equation without changing the solution.

If a, b and c are any three numbers

if a = b, then

1. a + c = b + c

2. a c = b c

Example 1

Solve for x

x + 2.7 = 8.9

Solution

Step 1:

To solve for x, we must isolate x. On left side of equation, we have x + 2.7; to isolate x, we must subtract 2.7.

Step 2:

From the additive property of equality with decimals we must subtract from both sides of an equation the same number. So, we subtract 2.7 from both sides as follows

x + 2.7 2.7 = 8.9 2.7

Step 3:

Simplifying

x = 8.9 2.7 = 6.2

So, x = 6.2

Example 2

Solve for x

x 1.3 = 11.7

Solution

Step 1:

To solve for x, we must isolate x. On left side of equation, we have x 1.3; to isolate x, we must add 1.3

Step 2:

From the additive property of equality with decimals we must add to both sides of an equation the same number. So, we add 1.3 to both sides as follows

x 1.3 + 1.3 = 11.7 + 1.3

Step 3:

Simplifying

x = 11.7 + 1.3 = 13.0

So, x = 13