Unit 3 Test 2 Corrections

Jerry tries to convince his classmate Frank that 2x = 14 represents an expression. Frank disagrees and thinks that it represents an equation. Who is correct?

• Jerry is correct because expressions contain variables.

• Frank is correct because equations always contain an equal sign.

• Both are correct because expressions and equations are the same thing.

• Neither of them is correct.

Answer explanation

Equations always contain an equal sign.

During the weekend, a local animal shelter took in 5 stray dogs. After these 5 dogs joined the shelter, the shelter had 104 dogs. Which equation can be used to find d, the number of dogs in the shelter before the 5 strays joined?

Answer explanation

To find the number of dogs before the 5 strays joined, we add the 5 strays to the number of dogs already in the shelter. Thus, the equation is d + 5 = 104, which correctly represents the situation.

The maximum speed limit on Beach St. is 40 miles per hour. Which of the following number lines best represents the legal speed(s) to travel?

• 
• 
• 
• 

Answer explanation

The closed dot indicates that drivers could go exactly 40 and the arrow pointing to the left (negative direction) indicates they could drive below 40.

• x ≤ 14
• x < 14
• x ≥ 14
• x = 14

Answer explanation

To solve the inequality 4x ≥ 56, divide both sides by 4. This gives x ≥ 14. The solution set includes all values of x that are 14 or greater.

Freddy has a goal of saving $60 for a video game. He saves $5 per week. Which inequality can Freddy use to determine t, the number of weeks he should save to meet or exceed his goal?

Answer explanation

Freddy saves $5 per week, so after t weeks he will have saved 5t dollars. To meet or exceed his goal of $60, the inequality is 5t ≥ 60, which means he needs to save at least that much.

Shaun made 3 times as many bracelets as necklaces. He made 36 bracelets. Write an equation that can be used to find the number of necklaces, x, that Shaun made.

• 2x = 36
• x = 12
• 3x = 36
• x + 3 = 36

Answer explanation

To solve the inequality y + 12 < 25, we subtract 12 from both sides, giving y < 13. The endpoint of the ray should be an open circle at 13, indicating 13 is not part of the solution. The ray points to the left, representing all values less than 13.

• Jenny had $24. She spent $8 on party decorations. What is x, the amount of money she had left?

• Jenny finished her cleaning chores in 24 minutes and her math homework in 8 minutes. What is x, the difference between the number of minutes spent doing cleaning chores and math homework?

• Jenny has been saving money from her allowance. Jenny spent $8 from her savings on a present for her mom and had $24 left. What is x, the amount of money Jenny had saved?

• Jenny earns $8 per hour. Last week she earned $24. What is x, the number of hours she worked last week?

Answer explanation

The equation x - 8 = 24 represents Jenny's savings. She spent $8 and had $24 left, so x (the total amount saved) is 24 + 8 = 32. This matches the scenario where she spent from her savings.

• {60, 15, 9, 3}

• {27, 25, 12, 10}

• {90, 60, 30, 3}

• {40, 38, 36, 34}

Answer explanation

To solve \( \frac{x}{3} < 10 \), multiply both sides by 3, giving \( x < 30 \). The set {27, 25, 12, 10} contains values all less than 30, making it the correct choice. Other sets include values 30 or greater.