Solving One-Variable Inequalities

Question 1

✔ x > –1.25x < –1.25x > –0.8x < –0.8

Revolt · Accepted Answer

A: ✔ x > –1.25

Question 2

Which number line represents the solution to 2.5 – 1.2x < 6.5 – 3.2x?

Revolt · Accepted Answer

C:

Question 3

Which student’s first step was incorrect, and why?

Revolt · Accepted Answer

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

Question 4

Which represents the solution set to the inequality ?

Revolt · Accepted Answer

D: (–∞, ]

Question 5

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

C: x = 0; E: x = 10

Question 6

What is the solution to (x + 8) > (2x + 10)?

Revolt · Accepted Answer

C: (–∞, 4)

Question 7

Question 7

Revolt · Accepted Answer

The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is .: 100 + 55x > 150 + 51x; The solution to the inequality is .: x > 12.5; Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.: 13

Question 8

✔ 100 + 55x > 150 + 51x100 + 55x < 150 + 51x100x+ 55 > 150x+ 51100x+ 55 < 150x+ 51

Revolt · Accepted Answer

A: ✔ 100 + 55x > 150 + 51x

Question 9

Question 9

Revolt · Accepted Answer

52.5

Question 10

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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