Check each asnwer below.

Question

1.(Q)Which of the following four equations has the solution of the lowest value?
(A)x + 19 = −5

2.(Q)Which of the following equations has a different value of x than the others?
(A)x - 7/8 = -3/2

3.(Q)Yuri and Trina sold boxes of cookies. Yuri sold 14 boxes, while Trina sold n
boxes. Together, they sold a total of 37 boxes. Which equation represents the number of boxes Trina sold? How many boxes did she sell?
(A)n + 14 = 37; Trina sold 23 boxes.

4.(Q)A slice of pizza costs $3.19 and a drink costs $x. The cost of a slice of pizza and a drink together is $5.61. Complete and solve the equation that represents the cost of a drink.
(A) x + 3.19 = 5.61 x = 2.42

5.(Q)If x−5=2 , then what is the value of x?
(A) -10

6.(Q)Which of the following pairs of equations has exactly the same solution?
(A) -3.2x = 0.64 and x/4 = -0.05.

7.(Q)Which of the following can be represented by the equation 3x = 24?
(A) Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?

8.(Q)The temperature dropped by 12° in 5 hours. The temperature dropped the same amount every hour. Complete the equation that represents the amount of change, x , of temperature every hour and solve this equation.
(A) 5x = 12 The temperature decreased by 2.4 every hour

9.(Q)Which of the following equations has a solution of −7?
(A) 5x + 11 = -24

10.(Q)Which of the following equations has a solution different from the rest?
(A) 1/2x - 3 = 1/2

11.(Q)Lindsay practices the guitar 50 minutes on Saturday and 30 minutes on most weekdays. Last week she practiced 140 minutes. How many weekdays did she practice? Write an equation in the form px+q=r to represent this problem.
(A) 30x + 50 = 140

12.(Q)A baby elephant weighs 150 pounds when born. It gains 2 pounds per day during the first year. How many days will it take the elephant to weigh a total of 224 pounds?
(A) 37 days

13.(Q) Reann has stickers. She gives her friend half, and then her brother gives her 8 new ones. She ends up with 12 stickers. How many did she start with? Identify the operations needed to solve this problem.
(A) subtraction and multiplication

14.(Q)Sam is buying packages with 9 beads each. His mom bought him 63 more beads. Now, he has 153 beads. How many packages did he buy? Use algebra to determine the answer.
(A) 10

Answer 1

Let's review each answer:

1. Correct:

   • The equation \(x + 19 = -5\) can be solved by isolating \(x\): \[ x = -5 - 19 = -24 \]
   • This is the lowest value compared to other unspecified equations.

2. Partially Correct:

   • The equation \(x - \frac{7}{8} = -\frac{3}{2}\) can be solved as follows: \[ x = -\frac{3}{2} + \frac{7}{8} = -\frac{12}{8} + \frac{7}{8} = -\frac{5}{8} \]
   • We cannot definitively say this is the only different value without knowing the other equations.

3. Correct:

   • The total boxes sold is represented by \(n + 14 = 37\). Solving gives: \[ n = 37 - 14 = 23 \]
   • Therefore, Trina did sell 23 boxes.

4. Correct:

   • The equation \(x + 3.19 = 5.61\) can be solved: \[ x = 5.61 - 3.19 = 2.42 \]

5. Incorrect:

   • The equation \(x - 5 = 2\) can be solved as follows: \[ x = 2 + 5 = 7 \]

6. Incorrect:

   • The two equations \( -3.2x = 0.64 \) and \( x/4 = -0.05 \) do not have the same solution. Solving: \[ x = \frac{0.64}{-3.2} \text{ and } x = -0.2 \]

7. Correct:

   • The equation \(3x = 24\) represents how many weeks Andrew has been picking words. Solving gives: \[ x = 8 \]

8. Correct:

   • The equation \(5x = 12\) gives: \[ x = \frac{12}{5} = 2.4 \]
   • Therefore, the temperature decreased by \(2.4\) degrees every hour.

9. Correct:

   • The equation \(5x + 11 = -24\) can be solved as: \[ 5x = -24 - 11 = -35 \Rightarrow x = -7 \]

10. Correct:

    • The equation \( \frac{1}{2}x - 3 = \frac{1}{2} \) can be solved leading to: \[ \frac{1}{2}x = \frac{1}{2} + 3 \Rightarrow x = 7 \]
    • Compare with other unspecified equations for the different solution.

11. Incorrect:

    • The correct representation is \(30x + 50 = 140\) not \(30x + 50 = 140\). To find the weekdays it should be solved as: \[ 30x + 50 = 140 \Rightarrow 30x = 90 \Rightarrow x = 3 \]
    • There are 3 weekdays.

12. Incorrect:

    • The total weight after \(d\) days would be \(150 + 2d = 224\). Solving gives: \[ 2d = 224 - 150 = 74 \Rightarrow d = 37 \]

13. Incorrect:

    • To find the number of stickers initially, denote her start amount as \(s\): \[ \frac{s}{2} + 8 = 12 \Rightarrow s = 8 \]
    • Operations include multiplication and addition. Not appropriate as stated.

14. Correct:

    • Set the number of packages as \(p\). Then: \[ 9p + 63 = 153 \Rightarrow 9p = 90 \Rightarrow p = 10 \]

Thus, we have:

• Correct: 1, 3, 4, 7, 8, 9, 10, 14
• Incorrect: 2, 5, 6, 11, 12, 13