Solving One-Variable Inequalities

Question 1

Which interval is the solution set to 0.35x – 4.8 < 5.2 – 0.9x?(–∞, –8)(–∞, 8)(–8, ∞)(8, ∞)

Revolt · Accepted Answer

(–∞, 8)

Question 2

The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is [___].

Revolt · Accepted Answer

100 + 55x > 150 + 51x; Selection 1: 100 + 55x > 150 + 51x; Selection 2: x > 12.5; Selection 3: 13

Question 3

Riko will be behind Yuto when 0 ≤ t < [___] minutes.

Revolt · Accepted Answer

52.5

Question 4

[___]

Revolt · Accepted Answer

> –1.25

Question 5

Which student’s first step was incorrect, and why?Amelia’s, because the variable term must be isolated on the left sideLuis’s, because he flipped the inequality sign when he subtractedShauna’s, because she did not apply the subtraction property of equality properly Clarence’s, because the terms he added together were not like terms

Revolt · Accepted Answer

Luis’s, because he flipped the inequality sign when he subtracted

Question 6

Which represents the solution set to the inequality ?x –1x (–∞, –1](–∞, ]

Revolt · Accepted Answer

(–∞, ]

Question 7

Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply. x = –1.1x = –2.2x = 0x = –10x = 10

Revolt · Accepted Answer

x = 0; x = 10

Question 8

Question 74567

Revolt · Accepted Answer

(–∞, –4); (–∞, 4)

Question 9

Yuto and Riko went for a bike ride on the same path. When Riko left their house, Yuto was 5.25 miles along the path. If Yuto’s average speed was 0.25 miles per minute and Riko’s average speed was 0.35 miles per minute, then Riko will be behind Yuto when 0 ≤ t < 52.5, where t is time in minutes. Explain what this solution means and why t cannot be less than zero.

Revolt · Accepted Answer

The solution 0 ≤ t < 52.5 means that Riko will be behind Yuto from the moment she leaves the house (t = 0) until she catches up to him at 52.5 minutes. Time cannot be less than zero because t represents the duration of the ride starting from the moment Riko leaves, and time cannot be negative.

Solving One-Variable Inequalities Answers

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