## 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 \(a-c=b-c\).**Addition Property of Equality**For all real numbers

*a, b,*and*c*,

if*a = b*then \(a+c=b+c\).

**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.