AnswersOnline Algebra Function Number AInequalities in One Variable

Inequalities in One Variable Answers

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Which did you include in your response? Check all that apply.

A
Multiplying or dividing by the same value on both sides of an equation does not change the solution set.
B
Multiplying or dividing by the same positive value on both sides of an inequality does not change the solution set.
C
Multiplying or dividing by the same negative value on both sides of an inequality changes the sense of the inequality.
3

What is the solution to the given inequality?

Question illustration
A
x –1
Option A
B
x ≤ –1
C
x ≥ 3
D
x ≤ 3
4

Which graph shows the correct representation of {x | x ≤ 5}?

A
[Image: A number line going from 4 to 6. An open circle ap...]
B
[Image: A number line going from 4 to 6. An open circle ap...]
C
[Image: A number line going from 4 to 6. A solid circle ap...]
D
[Image: A number line going from 4 to 6. A solid circle ap...]
5

The solution to an inequality is (–∞, 6.5]. Is 6.5 a solution to the inequality? Explain your answer.

A
The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution does not include 6.5.
B
The solution includes numbers from 6.5 to infinity. Because a parenthesis is used, the solution does not include 6.5.
C
The solution is the point (–∞, 6.5). Because a bracket is used, 6.5 is a solution to the inequality.
D
The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution includes 6.5.
6

Let x represent the number of canvases. Which inequality can be used to find x?

A
350 ≥ 125 + 15x
B
350 > 125 – 15x
C
350 ≤ 125 – 15x
D
350 < 125 + 15x
7

The club can buy up to 14 canvases.The club can buy at least 14 canvases. ✔ The club can buy up to 15 canvases.The club can buy at least 15 canvases.

A
The club can buy up to 14 canvases.
B
The club can buy at least 14 canvases.
C
✔ The club can buy up to 15 canvases.
D
The club can buy at least 15 canvases.
8

Which values are solutions to 90 < –30p + 15? Check all that apply.p = –10p = 0p = –2.5p = 3p = –5p = 7.6

A
p = –10
B
p = 0
C
p = –2.5
D
p = 3
E
p = –5
F
p = 7.6
9

The inequality 10.45b + 56.50 < 292.67 is used to find the number of boxes (b) that can be loaded on a truck without exceeding the weight limit of the truck. The solution is written as {b | b < 22.6}. Which statement best describes the meaning of the solution?

A
The truck can hold more than 22 boxes.
B
The truck can hold more than 23 boxes.
C
The truck can hold up to 22 boxes.
D
The truck can hold up to 23 boxes.
10

The temperature of magnesium must be at least 650 degrees for the metal to melt. A sample of magnesium is currently 255 degrees. The temperature of the magnesium is increased by 10 degrees every minute. Which inequality shows the number of minutes (m) needed to raise the temperature to the melting point?

A
m > 39.5
B
m ≥ 39.5
C
m > 87.5
D
m ≥ 87.5
11

Explain the differences between properties of equality and properties of inequality when solving equations and inequalities.

Answer:

Properties of equality let you perform the same operation on both sides of an equation without changing its solution set. For inequalities, adding or subtracting the same value or multiplying or dividing by a positive value preserves the inequality’s direction. When multiplying or dividing by a negative value, you must reverse the inequality symbol.

12

Which inequality is true for all real numbers? Check all that apply.a – b d, then a– c < a – dIf a < b, then a < b + c

A
a – b < a + b
B
ac ≥ bc
C
If a ≥ b, then a + c ≥ b + c
D
If c > d, then a– c < a – d
E
If a < b, then a < b + c

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