1. LT: I can solve and graph inequalities.
Entry Task
Solve for the given variable
1) A = ½bh for h
2) ax + bx = c solve for x
LT: I can solve and graph inequalities.

2. LT: I can solve and graph inequalities.
1.5 Solving Inequalities
Target: I can solve and graph inequalities. Write and solve compound inequalities.
LT: I can solve and graph inequalities.

3. LT: I can solve and graph inequalities.
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.
LT: I can solve and graph inequalities.

4. Review of Inequality Signs
> greater than
< less than
greater than or equal
less than or equal
LT: I can solve and graph inequalities.

5. 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
LT: I can solve and graph inequalities.

6. LT: I can solve and graph inequalities.
Solve the inequality:
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
LT: I can solve and graph inequalities.

7. 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.
LT: I can solve and graph inequalities.

8. LT: I can solve and graph inequalities.
Example:
Solve: -3y + 5 >23
-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
LT: I can solve and graph inequalities.

9. LT: I can solve and graph inequalities.
2x < -6 and 3x ≥ 12
Solve each inequality for x
Graph each inequality
Combine the graphs
Where do they intersect?
They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -3 -6 o -3 -6 o 4 7 1 o ● 4 7 1 o ●
LT: I can solve and graph inequalities.

10. Graph 3 < 2m – 1 < 9
Remember, when written like this, it is an AND problem!
3 < 2m – 1 AND 2m – 1 < 9
Solve each inequality.
Graph the intersection of 2 < m and m < 5. 5 -
LT: I can solve and graph inequalities.

11. LT: I can solve and graph inequalities.
Subtract 12 from both sides
Simplify
Divide both sides by -3
Simplify (Switch the inequality!)
Check your answer
Graph the solution
-3a > 6
a < -2
12 - 3(-2) = 18 o -2 -1 -3
LT: I can solve and graph inequalities.

12. LT: I can solve and graph inequalities.
Solve p - 20 > 14p + 64
Subtract 14p from both sides
Simplify
Add 20 to both sides
Divide both sides by 12
Check your answer
Graph the solution
-14p p
12p – 20 > 64
12p > 84
p > 7
26(7) – 20 = 14(7) + 64 o 7 8 6
LT: I can solve and graph inequalities.

13. LT: I can solve and graph inequalities.
Try these:
Solve 2x+3>x+5
Solve - c - 11>23
Solve 3(r-2)<2r+4
LT: I can solve and graph inequalities.

14. LT: I can solve and graph inequalities.
Assignment
Wkst 1.5 #’s 1,4,5,7,9,11-14,19,21,22,25,26,27
LT: I can solve and graph inequalities.