Key Concepts

Key Concepts

• To Determine Whether a Number is a Solution to an Equation
  
  1. Substitute the number in for the variable in the equation.
  2. Simplify the expressions on both sides of the equation.
  3. Determine whether the resulting statement is true.
     • If it is true, the number is a solution.
     • If it is not true, the number is not a solution.
• Addition Property of Equality
  
  • For any numbers a, b, and c, if \(a=b\), then \(a+c=b+c\).
• Subtraction Property of Equality
  
  • For any numbers a, b, and c, if \(a=b\), then \(a-c=b-c\).
• To Translate a Sentence to an 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.
• To Solve an Application
  
  1. Read the problem. Make sure all the words and ideas are understood.
  2. Identify what we are looking for.
  3. Name what we 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 the important information.
  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.