Math 152
Chapter 4 Handout
Helene Payne
Name:
1. Write each interval on set-builder notation, then graph the interval on
the numberline.
(a) (2, 5)
on setbuilder notation: {
x
(b) [−3, 3)
on setbuilder notation: {
x
(c) [0, 4]
on setbuilder notation: {
x
2. Solve each linear inequality. Graph the solution on the numberline,
then give the solution on interval notation.
(a) 2x + 9 ≤ 11
x
Solution on interval notation:
Math 152
Chapter 4 Handout
Helene Payne
(b) −3x − 5 > 4
x
Solution on interval notation:
(c) 5x + 2 ≥ 3x + 10
x
Solution on interval notation:
3. Set up the following problems as an inequality, DO NOT SOLVE IT!!
When making a long-distance call from a certain pay phone, the first
three minutes of a call cost $3.00. After that, each additional minute or
portion of a minute cost $0.20. Let x be the number of minutes of a long
distance call. Use an inequality to find the maximum number of minutes
one can call long distance for $5.80.
Page 2
Math 152
Chapter 4 Handout
Helene Payne
4. Use the following sets to find the union or intersection.
A = {1, 3, 5, 7, 9}
B = {1, 2, 3, 4, 5}
C = {2, 4, 6, 8}
(a) A ∪ B = {
}
(b) A ∪ C = {
}
(c) A ∩ B = {
}
(d) A ∩ C = {
}
5. Solve each compound linear inequality. Graph the solution on the numberline, then give the solution on interval notation.
(a) x > 2 and x > 4
x
Solution on interval notation:
(b) x ≥ 3 or x < −2
x
Solution on interval notation:
Page 3
Math 152
Chapter 4 Handout
Helene Payne
(c) 2x − 3 < −7 or −2x + 11 < 21
x
Solution on interval notation:
(d)
−4x + 2
> 6 and 3x − 1 > −22
3
x
Solution on interval notation:
6. The formula for converting Celsius temperature, C, to Fahrenheit temperature, F , is F = 1.8C + 32.
(a) Solve the formula for C.
C=
(b) If Celsius temperature ranges from 45◦ to 115◦ , inclusive, express
this as a compound inequality in C:
(c) Substitute in the expression for C, found in part (a), then solve the
inequality to find the range for the Fahrenheit temperature. Give
the answer in interval notation.
Page 4
Math 152
Chapter 4 Handout
Helene Payne
7. Solve each absolute value equation. Give the solutions on roster notation!
(a) |x − 3| = 8
Solution: {
(b) |x| = −7
Solution: {
(c) 3|x + 2| − 2 = 7
Solution: {
8. Solve each absolute value inequality. Graph the solution on the number
line, then give the solution on interval notation!
(a) |x| < 2
x
Solution on interval notation:
Page 5
Math 152
Chapter 4 Handout
Helene Payne
(b) |x − 6| ≥ 2
x
Solution on interval notation:
3x − 4 >1
(c) 2 x
Solution on interval notation:
(d) 2|3 − 2x| + 5 ≤ 3
x
Solution on interval notation:
Page 6
Math 152
Chapter 4 Handout
9. Graph each linear inequality.
(a) x + y < −3
(b) y ≥ 2
10. Graph the solution set of the system of linear inequalities.
(a) 3x + 2y ≥ 5
(b) y > x + 2
2x − y < 8
y < −2x + 5
Page 7
Helene Payne
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