## Key Concepts

**Determine whether a number is a solution to an equation.**

- Substitute the number for the variable in the equation.
- Simplify the expressions on both sides of the equation.
- 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.

**Subtraction and Addition Properties of Equality**

**Subtraction Property of Equality**

For all real numbers * a, b,* and *c*,

if * a = b* then [latex]a-c=b-c[/latex] .

**Addition Property of Equality**

For all real numbers * a, b,* and *c*,

if * a = b* then [latex]a+c=b+c[/latex] .

**Translate a word sentence to an algebraic equation.**- Locate the “equals” word(s). Translate to an equal sign.
- Translate the words to the left of the “equals” word(s) into an algebraic expression.
- Translate the words to the right of the “equals” word(s) into an algebraic expression.

**Problem-solving strategy**- Read the problem. Make sure you understand all the words and ideas.
- Identify what you are looking for.
- Name what you are looking for. Choose a variable to represent that quantity.
- Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.
- Solve the equation using good algebra techniques.
- Check the answer in the problem and make sure it makes sense.
- Answer the question with a complete sentence.

## Glossary

**solution of an equation**- A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.