Summary: Solving Equations Using the Subtraction and Addition Properties of Equality
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.
Licenses & Attributions
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].