1. Solving Inequalities and Absolute Value Equations Introduction Lessons Algebra 2 – Lesson 1

2. > greater than or equal
Solving inequalities follows the same procedures as solving equations. There are a few special things to consider with inequalities: We need to look carefully at the inequality sign. We also need to graph the solution set.
Sometimes you may have to reverse the direction of the inequality sign!! That only happens when you
multiply or divide both sides of the inequality by a negative number.
> greater than
< less than
> greater than or equal
< less than or equal

3. How to graph the solutions of inequalities
x > Graph any number greater than. . .
open circle, line to the right
x < Graph any number less than. . .
open circle, line to the left
x > Graph any number greater than or equal to. . .
closed circle, line to the right
x < Graph any number less than or equal to. . .
closed circle, line to the left

4. Solve and graph on a number line.
A) 2x+3>x B) -2c - 11>23 C) 3(r-2)<2r+4

5. Solve and graph on a number line.
D) 3x + 5 > E) 7x + 3 < 18x – F) 2x > x x 3

6. Solving Absolute Value Equations
First, isolate the absolute value expression.
Remember Absolute Value is always positive!
Set up two equations to solve.
Consider the equation | x | = 3. The equation has two solutions since x can equal 3 or -3.
For the first equation, drop the absolute value bars and solve the equation.
For the second equation, drop the bars, negate the opposite side, and solve the equation.
Always check the solutions!!!
Solve |x + 8| = 3

7. Solve each absolute value equation.
|y + 4| - 3 = B) |3d - 9| + 6 = 0
C) 3|x - 5| = 12

8. Solve each absolute value equation.
D) 6|5x + 2| = E) 3|x + 2| -7 = 14
F) |x – 2| = 2x - 10