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.
1.5 Solving Inequalities
Target: I can solve and graph
inequalities.
Write and solve compound inequalities.
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.
Review of Inequality Signs
> greater than
< less than
 greater than or equal
 less than or equal
LT: I can solve and graph
inequalities.
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.
Solve the inequality:
x+4<7
-4 -4
x < 3
Subtract 4 from each side.
Keep the same inequality sign.
Graph the solution.
Open circle, line to the left.
0
3
LT: I can solve and graph
inequalities.
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.
Example:
Solve: -3y + 5 >23
Subtract 5 from each side.
-5 -5
-3y > 18
-3
-3
y < -6
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.
0
2x < -6 and 3x ≥ 12
1.
2.
3.
4.
5.
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!!
2 x 6

2
2
x  3
-3
3x 12

3
3
x4
0
1
7
LT: I can solve and graph
inequalities.
-6
o
o
●
4
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
0
LT: I can solve and graph
inequalities.
5
1.
2.
3.
4.
5.
6.
Solve 12 - 3a > 18
- 12
- 12
Subtract 12 from both
sides
Simplify
-3a > 6
Divide both sides by -3
Simplify
-3
-3
(Switch the inequality!)
Check your answer
a < -2
Graph the solution
12 - 3(-2) = 18
-3
o
-2
LT: I can solve and graph
inequalities.
-1
Solve
1.
2.
3.
4.
5.
6.
7.
8.
26p - 20 > 14p + 64
Subtract 14p from both
sides
Simplify
Add 20 to both sides
Simplify
Divide both sides by 12
Simplify
Check your answer
Graph the solution
6
o
7
-14p
-14p
12p – 20 > 64
+ 20
+ 20
12p
> 84
12
12
p>7
26(7) – 20 = 14(7) + 64
LT: I can solve and graph
inequalities.
8
Try these:
Solve 2x+3>x+5
Solve - c - 11>23
Solve 3(r-2)<2r+4
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.