Help 1. Solve the equation.
5(x – 4) + 3x – 9x = 6 – (2x + 5) + 8x
Step 1: Use the distributive property to remove the parentheses. (2 points)

Step 2: Collect any like terms on both sides of the equation. (2 points)

Step 3: Bring all variable terms to one side of the equation. (Hint: Add x to both sides.) (2 points)

Step 4: Bring all the constant terms to one side. A constant term is a number without a variable. (2 points)

Step 5: Now solve for x. Show your work. (2 points)

2. Solve each inequality for the variable. Show your work. (8 points: 2 points each with work shown)
A.

C. 13c ≤ –169

B. 5b – 28 > 27

D. 3x – 7 ≥ 4x + 2

3. Your school football team wants to make a new banner to display at the district tournament. The rectangular banner will be dark red, with a white ribbon border. The length of the banner needs to be 15 feet. What are the possible widths of the banner if the length of ribbon available is 46 feet?
Part A: Write and solve an inequality to find the possible widths of the banner.
The ribbon goes around the outside of the banner. The banner has a length of 15 feet and an unknown width. Write an expression to describe the length of ribbon that will be needed. Remember, the perimeter of a rectangle is twice the length plus twice the width. Use w to represent the width. (2 points)

The length of ribbon available is 46 feet. Write an inequality that compares your expression from part 1 with the length of ribbon available. (1 point)

Use the inequality from part 2 to solve for the width of the banner. (2 points)

Write your answer in a sentence. (1 point)

Part B: Assume that the banner needs to be 18 feet long instead of 15 feet. How wide can it be to have enough ribbon to go around?
Rewrite the inequality using an 18-foot length instead of 15 feet. (1 point)

Solve this inequality for w. (2 points)

Write your answer as a sentence. (1 point)

4. Solve each equation for x. (8 points: 2 points each)
a. 3x – 12y = 27

c. 4x – k = 17

b. 6x – 7y = –2

d. kx + c = 9

5. A can has a radius of 2 inches and a volume of 62.8 cubic inches. Find the height of the can.
The formula for the volume of a cylinder is V = πr2h. Rewrite this formula to solve for h. (2 points)

Use your formula to find the height, h, of the can. Use 3.14 for π. (2 points)

Write your answer as a sentence. (1 point)

6. Clare spent a total of 25 minutes at the track. She spent 5 minutes stretching and walked 4 laps around the track. If she walked at a constant pace, how long did it take her to walk each lap? What was her pace in inches per second?
Write an equation to represent the time Clare spent at the track. Use x to represent the time it took her to walk one lap. (1 point)
+ x =
Solve the equation for x to find the time it takes Clare to walk one lap. (2 points)

After Clare walked one lap around a track, her fitness tracker measured the distance as 0.272 miles. The actual distance of the track is 0.25 miles. Is her tracker accurate? Is it precise? Explain your answer. (2 points)

Convert 0.272 miles to inches. According to her fitness tracker, how many inches did Clare walk? Round your answer to the nearest inch. (2 points)
HINT: There are 5280 feet in 1 mile, and 12 inches in 1 foot.

Convert 5 minutes to seconds. (1 point)

Divide the number of inches (from part d) by the number of seconds (from part e) to find Clare's walking rate in inches per second. (1 point)