Solving One-Variable Inequalities: Assignment

Which interval is the solution set to 0.35x - 4.8 < 5.2 - 0.9x?

B. (-∞, -8)

Which of the x values are solutions to the inequality 4(2 - x) > -2x - 3(4x + 1)? Check all that apply.

3. x = 0 5. x = 10

Yuto left his house at 10 a.m. to go for a bike ride. By the time Yuto's sister Riko left their house, Yuto was already 5.25 miles along the path they both took. If Yuto's average speed was 0.25 miles per minute and Riko's average speed was 0.35 miles per minute, over what time period in minutes, t, starting from when Riko left the house, will Riko be behind her brother? Riko will be behind Yuto when 0 ≤ t < ____ minutes.

52.5

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality7.2b + 6.5 > 4.8b - 8.1. Amelia started by subtracting 7.2b from both sides to get 6.5 > -2.4b - 8.1. Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < - 8.1. Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b - 14.6. Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b. Which student's first step was incorrect, and why?

B. Luis's, because he flipped the inequality sign when he subtracted

Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. How many months will it take for the second phone to be less expensive than the first phone? The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is ________ The solution to the inequality is ________ Sal's mother would have to keep the second cell phone plan for at least _____ months in order for it to be less expensive.

Blank One: 100+55x>150+51x Blank Two: x>12.5 Blank Three: 13

Which represents the solution set to the inequality -1.5(4x+1)≥4.5-2.5(x+1)

C. (-∞, -1]

What is the solution to 3/4(x + 8) > 1/2(2x + 10)?

C. (-∞, 4)

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

C. Line three

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.

Sample Answer: The solution means that Riko will be behind Yuto from the time she leaves the house, which corresponds to t = 0, until the time she catches up to Yuko after 52.5 minutes, which corresponds to t = 52.5. The reason that t cannot be less than zero is because it represents time, and time cannot be negative.

Complete the steps to solve the inequality: 0.2(x + 20) - 3 > -7 - 6.2x Use the distributive property: Combine like terms: Use the addition property of inequality: Use the subtraction property of inequality: Use the division property of inequality: 0.2x + 4 - 3 > -7 - 6.2x 0.2x + 1 > -7 - 6.2x 6.4x + 1 > -7 6.4x > -8

x>-1.25