- Equations and Applications
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- Additive property of equality with decimals
- Multiplicative property of equality with decimals
- Multiplicative property of equality with whole numbers: Fractional answers
- Multiplicative property of equality with fractions
- Using two steps to solve an equation with whole numbers
- Solving an equation with parentheses
- Solving a fraction word problem using a linear equation of the form Ax = B
- Translating a sentence into a multi-step equation

# Additive property of equality with decimals

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

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

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