SOLVING MULTI-STEP INEQUALITIES
TWO STEP INEQUALITIES
Solve: 2x – 3 < 13+3 +3
2x < 16 2 2
x < 8
CHECK!
SOLVING MULTI-STEP INEQUALITIES
TWO STEP INEQUALITIES
Solve: 5 – 3x < 20-5 -5
-3x < 15 -3 -3
x > - 5
CHECK!
DING!
SOLVING MULTI-STEP INEQUALITIES
Solve: 5(x – 3) + 2 < 12
+13 +13
5x < 25 5 5
x < 5
CHECK!
5x – 15 + 2 < 12
5x – 13 < 12
SOLVING MULTI-STEP INEQUALITIES
Solve: 5 + 3(7 – x) > 32
-26 -26
-3x > 6 -3 -3
x < -2
CHECK!
5 + 21 – 3x > 32
26 – 3x > 32
DING!
SOLVING COMPOUND INEQUALITIES
Graph the solution sets for:
x < 2 or x > 7
x < 2 and x > 7
x > 2 and x < 7
x > 2 or x < 7
2 7
2 7NO SOLUTION
2 7
2 7ALL REALS
SOLVING COMPOUND INEQUALITIES
A compound inequality containing “and” is true only if both inequalities
are true.
So, the graph of a compound inequality containing “and” is the
INTERSECTION of the graphs of the two inequalities.
SOLVING COMPOUND INEQUALITIES
Solve and graph the solution set:
x + 5 > 2 and x - 3 < 7 -5 -5
x > -3 and x < 10 +3 +3
-3 10
SOLVING COMPOUND INEQUALITIES
Solve and graph the solution set:
6 < x + 2 < 12
4 10
-2 -2 -2
4 < x < 10
SOLVING COMPOUND INEQUALITIES
A compound inequality containing “or” is true only if one or more of the
inequalities is true.
So, the graph of a compound inequality containing “or” is the UNION of the graphs of the two
inequalities.
SOLVING COMPOUND INEQUALITIES
Solve and graph the solution set:
2x – 3 < 7 or 3 – x < -8
5 11
+3 +3
2x < 10 or -3 -3
-x < -11 2 2
x < 5 or
-1 -1
x > 11
DING!
SOLVING COMPOUND INEQUALITIES
Try These:Solve and graph the solution set:
10 < x + 3 < 22 -3 -3 -3
7 < x < 19
7 19
SOLVING COMPOUND INEQUALITIES
Try These:Solve and graph the solution set:
2x + 3 < 9 or 5 – x < -2 -3 -3
2x < 6 2 2
x < 3
or
-5 -5
-x < -7 -1 -1
“ding”
or x > 7
3 7
SOLVING COMPOUND INEQUALITIES
Try These:Solve and graph the solution set:
x + 6 > 2 and x - 8 < 7 -6 -6
x > - 4 and
+8 +8
x < 15
- 4 15
SOLVING COMPOUND INEQUALITIES
Try These:Solve and graph the solution set:
3x > 9 or x + 6 < 7 3 3
x > 3 or
-6 -6
x < 1
1 3
SOLVING COMPOUND INEQUALITIES
Working backwards:Write the compound inequality for
the following graphs:
0 2 4 6-2-4-6
x > -2 and x < 4
OR -2 < x < 4
SOLVING COMPOUND INEQUALITIES
Working backwards:Write the compound inequality for
the following graphs:
0 2 4 6-2-4-6
x < 1 or x > 3
SOLVING COMPOUND INEQUALITIES
Working backwards:Write the compound inequality for
the following graphs:
0 2 4 6-2-4-6
-2 < x < 4
x > -2 and x < 4
SOLVING COMPOUND INEQUALITIES
Working backwards:Write the compound inequality for
the following graphs:
0 2 4 6-2-4-6
x < - 4 or x > 4
SOLVING COMPOUND INEQUALITIES
Working backwards:Write the compound inequality for
the following graphs:
0 2 4 6-2-4-6
0 < x < 1
x > 0 and x < 1
