Download Solving Linear Inequalities

A2 – Section 1.6
Date__________________
Solving Linear Inequalities
Linear Inequalities: inequalities with only ______________________
Graph by using:
< or >
x > -3
< or >
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
x < -1
Transformations that produce equivalent inequalities:
Transformation Applied
Original Inequality
Add the same number to each side.
x–5>9
Subtract the same number from each side.
x + 4 < -2
Multiply each side by a positive number.
⅛x < -3
Divide each side by a positive number.
7x > 35
Multiply each side by a negative number.
REVERSE the inequality!!
Divide each side by a negative number.
REVERSE the inequality!!
-x < 12
Ex 1
a)
-6
Solve and graph.
11x – 9 > 13
-4
-2
0
2
-6x > 42
b)
4
6
Equivalent Inequality
7x + 9 > 10x – 12
-4
-2
0
2
4
6
8
Compound Inequality: ______ simple inequalities joined by ______ or ____
Ex 2 Graph the following compound inequalities.
a) -5 < x < 2
b) x < -3 or x > 3
-6
-4
-2
0
2
4
6
-4
-2
0
2
4
6
8
Solve and graph each of the compound inequalities.
AND – Apply inverse operations to each
OR - Solve and graph each simple
section of the inequality!
inequality separately.
Ex 2 -9 < y + 4 < 10
Ex 3 -2x + 7 < 3 or 3x + 5 < 2
Ex 4 Write an inequality that satisfies the following conditions.
a) Milk will stay a liquid and keep until its
b) The yoga studio charges $22 per month
expiration date if it’s stored between -1ºC for membership and $5.50 for each yoga
and 5ºC.
class that you attend. If you budget $66 a
month for yoga classes, how many classes
may you attend each month?
Question: How is the process for solving and graphing linear inequalities similar to the
process of solving and graphing linear equations? How are the processes different?