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AFDA
4-3: Compound Inequalities
* Class work *
1
***Don’t forget to switch the inequality symbol when multiplying or dividing by a negative number!!!
When determining how to graph, separate the compound inequality into two inequalities
“AND” – Whatever you do in the middle, you do to all three parts! {Barbell}
“OR” - Solve each inequality separately; graph on same number line {Fly aways}
1.)
Graph each of the following inequalities:
a. -11  v  2
c. x < -2 and x  9
2.)
b. x < 3 or x > -10
d. m > 6 or m  -8
Solve each inequality and graph each solution.
a.
5  x  1  4
b.
2  3x  13 or 4x  2x  6
c.
-2 < x + 5 < 4
d.
x  4  1 or  3x  27
AFDA
4-3: Compound Inequalities
* Class work *
p
e.
p – 2 ≤ -2 or
g.
8  2 x  1  12
h.
x – 4 < -6 or -3x < -12
i. 6 < 2(x – 1) < 10
j.
3x + 2 < -10 or -x – 1 < 1
k. –5 < 3 – 2x < 11
l. 3x – 4 < 5 or 2x – 6 > 6
3
–2>1
f. -9 < -3(x + 2) < 12
2
AFDA
4-3: Compound Inequalities
* Class work *
3)
3
Circle the connecting word and then translate the verbal phrase into an inequality. {And/Or}
a.
All real numbers that are less than -1 or greater than or equal to 4
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b.
All real numbers that are greater than or equal to -3 and less than 5
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c.
Three less than x is greater than -4 and less than -1.
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d.
The quantity x  4 is greater than 14 or it is less than 8.
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e.
2x  1 is less than 1 or the product of 5 and x is greater than 10.
___________________________________
3.) Read each situation presented and write the appropriate inequality.
a.
All of the possible bids at an auction if the lowest bid for an autographed trading card is $20 and
the highest bid is $54.
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b.
All of the possible temperatures if the high temperature in a city last year was 95° F and the low
temperature was -5° F.
___________________________________
c.
The temperature at the a football game is uncomfortable if the temperature is lower than 55oF or
higher than 82oF
___________________________________
d.
The ages of the students in this class are greater than 12 and less than 16
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AFDA
4-3: Compound Inequalities
* Class work *
e.
4
The cost of cell phones are either less than $60 or more than $110
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f.
Children are not allowed in the playhouse if they are shorter than 30 inches or taller than 48
inches.
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4. Write an inequality which describes each graph.
a.
b.
–6 –4
–2
0
2
4
6
c.
–6
–4
–2
0
2
4
6
–6
–4
–2
0
2
4
6
d.
–6 –4
–2
0
2
4
6