Additive property of equality with decimals
Definition
The additive property of equality states that we can add (or subtract) the same number (or algebraic expression) 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