Key Concepts

Determine whether a number is a solution to an equation.

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

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.
  1. Locate the “equals” word(s). Translate to an equal sign.
  2. Translate the words to the left of the “equals” word(s) into an algebraic expression.
  3. Translate the words to the right of the “equals” word(s) into an algebraic expression.

• Problem-solving strategy
  1. Read the problem. Make sure you understand all the words and ideas.
  2. Identify what you are looking for.
  3. Name what you are looking for. Choose a variable to represent that quantity.
  4. 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.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. 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.