3-1

3-1 Linear Inequalities; Absolute Value

In this lesson, we learned how to solve and graph linear inequalities with one variable. Solving linear inequalities is very similar to solving linear equations.

-You can add/subtract the same number to both sides of an inequality.

-You can multiply/divide both sides of an inequality by the same positive number.

-You can multiply/divide both sides of an inequality by the same negative number if you reverse the inequality sign.

Example 1: 8x + 6 > 30

• 8x > 24 (I subtracted the 6 from 30.)
• x > 3 (I divided 24 by 8.)

Example 2: lxl > -2

• x > -2 x < 2

Example 3: 3x - 4 < 10 + x

• 3x < 14 + x (I added the 4 to 10.)
• 2x < 14 (I subtracted the x from 3x.)
• x < 7 (I divided 14 by the 2.)