Homework 3 - Section 2.5 #5
Intermediate Algebra / MAT 135 Fall 2016 possible master (Prof. Fleischner)
Student Name/ID:
1. Write the following as an inequality.
−6 is less than x, and
9 is greater than or equal to x
Use x only once in your inequality.
2. Write the following as an inequality.
0 is less than or equal to x, and
6 is greater than or equal to x
Use x only once in your inequality.
3. Graph the compound inequality on the number line.
x ≤ −5 or x > 8
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
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4. Graph the compound inequality on the number line.
x > −4 and x ≤ 1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
5. Write a compound inequality for the graph shown below.
Use x for your variable.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
7 8 9 10 x
6. Write a compound inequality for the graph shown below.
Use x for your variable.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
7 8 9 10 x
7. The sets E and F are defined as follows.
E = x |x ≤ 2
F = x |x > 8
Write E ∩ F and E ∪ F using interval notation.
If the set is empty, write ∅.
D
E
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8. The sets D and E are defined as follows.
D = v |v < 3
E = v |v ≤ 5
Write D ∪ E and D ∩ E using interval notation.
If the set is empty, write ∅.
9. Solve the compound inequality.
4x + 2 ≥ −10 and 3x − 4 < 8
Graph the solution on the number line.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
10. Solve the compound inequality.
−12 ≤ 4x + 4 < 16
Graph the solution on the number line.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
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11. Solve the compound inequality.
4v − 3 < −23
and
2v + 2 ≤ 14
Write the solution in interval notation.
If there is no solution, enter ∅.
12. Solve the compound inequality.
2w − 3 ≤ 5
or
4w − 6 < −10
Write the solution in interval notation.
If there is no solution, enter ∅.
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Homework 3 - Section 2.5 #5 Answers for class Intermediate
Algebra / MAT 135 Fall 2016 possible master
1. −6 < x ≤ 9
2. 0 ≤ x ≤ 6
3.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
9 10
4.
5. −5 ≤ x < 7
6. x < 0 or x ≥ 2
7. E ∩ F = ∅
E ∪ F = − ∞ , 2 ∪ 8, ∞
8. D ∪ E = − ∞ , 5
D ∩ E = − ∞, 3
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9.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
10.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
11. − ∞ , −5
12. − ∞ , 4
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