## Key Concepts

**How to determine whether a number is a solution to an equation.**- Step 1. Substitute the number for the variable in the equation.
- Step 2. Simplify the expressions on both sides of the equation.
- Step 3. Determine whether the resulting equation is true.
- If it is true, the number is a solution.
- If it is not true, the number is not a solution.

**Properties of Equalities**Subtraction Property of Equality Addition Property of Equality \(\text{For any numbers}\phantom{\rule{0.2em}{0ex}}a,b,c,\) \(\text{if}\phantom{\rule{0.2em}{0ex}}a=b\phantom{\rule{0.2em}{0ex}}\text{then}\phantom{\rule{0.2em}{0ex}}a-c=b-c.\)

\(\text{For any numbers}\phantom{\rule{0.2em}{0ex}}a,b,c,\) \(\text{if}\phantom{\rule{0.2em}{0ex}}a=b\phantom{\rule{0.2em}{0ex}}\text{then}\phantom{\rule{0.2em}{0ex}}a+c=b+c.\)

**Division Property of Equality**- For any numbers \(a,b,c,\) and \(c\ne 0\)
If \(a=b\), then \(\frac{a}{c}=\frac{b}{c}\).

- For any numbers \(a,b,c,\) and \(c\ne 0\)