1. Solving Inequalities
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.

2. Review of Inequality Signs
> greater than
< less than
greater than or equal
less than or equal

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

4. Solve the inequality: -4 -4 x < 3 x + 4 < 7
x < 3
Subtract 4 from each side.
Keep the same inequality sign.
Graph the solution.
Open circle, line to the left. 3

5. Can we always undo and keep the inequality true?
Let’s investigate:
2 < 6
Adding to both sides?
2 + 2 < 6 + 2
Subtracting on both sides?
2 – 2 < 6 - 2

6. Can we always undo and keep the inequality true?
Let’s investigate:
2 < 6
Multiply both sides?
2 ∙ 2 < 6 ∙ 2
Dividing on both sides?
< 6 2

7. So far so good?
What about multiplying and dividing by a negative number?:
2 < 6
Multiply both sides by -2?
2 ∙ -2 < 6 ∙ -2
If we multiply or divide by a negative number we need to flip the inequality sign.

8. There is one special case.
You only reverse the inequality sign when when you multiply or divide both sides of the inequality by a negative number.

9. Example: -3y > 18 Solve: -3y + 5 >23 -5 -5
-3y > 18
y < -6
Subtract 5 from each side.
Divide each side by negative 3.
Reverse the inequality sign.
Graph the solution.
Open circle, line to the left. -6

10. Try these:
Solve 2x+3>x+5
Solve - x - 11>23
Solve

11. Homework: