1. Solving Inequalities

2. Solving Inequalities
Solving inequalities follows the same procedures as solving equations with 2 new rules.
The sign (direction) of the inequality changes when:
You multiply or divide by a negative number
You swap positions of the variable and answer

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

4. 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

5. 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

6. There is one special case.
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.

7. 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

8. Try these:
Solve 2x+3>x+5
Solve - c - 11>23
Solve 3(r-2)<2r+4

9. Properties of Inequalities
Transitive Property
If a b and b c, then a c
Addition Property
If a b then a + c b + c
Subtraction Property
If a b then a –c b - c

10. Properties of Inequalities
Multiplication Property
If a < b, and c > 0, then ac < bc
If a < b, and c < 0, then ac > bc
Division Property
If a < b, and c > 0, then a/c < b/c
If a < b, and c < 0, then a/c > b/c