1. Solving Linear Inequalities A Linear Equation in One Variable is any equation that can be written in the form: A Linear Inequality in One Variable is any inequality that can be written in one of the following forms:

2. 1) Solve the linear inequality in the same way you would solve a linear equation. 2) Exception! Switch the direction of the inequality sign if you: a)Multiply both sides by a negative value Solving a Linear Inequality b) Divide both sides by a negative value

3. Example 1 Use the same steps as you would in solving an equation. Solve

4. Note that in solving this inequality we never did multiply or divide by a negative value. Thus, there were no exceptions in this problem.

5. Example 2 Simplify each side. Solve

6. Combine the variable terms. Note that we added a negative quantity to both sides, but this is not an exception We have an exception to the rules for solving linear equations only when we multiply or divide both sides by a negative value.

7. Isolate the x.

8. Our next step is to divide both sides by the coefficient of – 7. Since we are dividing by a negative number, we have an exception! Switch the direction of the inequality sign!

9. The solution is …

10. 1) Solve the linear inequality in the same way you would solve a linear equation. 2) Exception! Switch the direction of the inequality sign if you: a)Multiply both sides by a negative value Summary for Solving a Linear Inequality b) Divide both sides by a negative value

11. Example 3 Multiply every term by the common denominator … Solve

12. Combine the variable terms.

13. Divide both sides by the coefficient of the variable Since we are dividing by a negative number, we have an exception! Switch the direction of the inequality sign!

14. The solution is …