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Question 1

A)What is the first step in solving the equation 20 = 6x − 4 solving for x?(1 point)
Responses

Subtract 20 from both sides.
Subtract 20 from both sides.

Add 4 to both sides.
Add 4 to both sides.

Subtract 4 from both sides.
Subtract 4 from both sides.

Divide both sides by 6.
Divide both sides by 6.
Question 2
A)Shawnece is solving the equation x7 − 4 = −6. One of her steps is to multiply both sides of the equation by 7. Why? (1 point)
Responses

Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the addition in the original problem.

The negative sign in −6 must be changed to positive.
The negative sign in negative 6 must be changed to positive.

Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the subtraction in the original problem.

Multiplying both sides by 7 undoes the division of x
by 7 in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
Question 3
A)Tillie is solving an equation for x
. Her first step is to subtract 8 from both sides of the equation. Which equation is she solving?(1 point)
Responses

12 = −x − 8
12 equals negative x minus 8

12 = −x + 8
12 equals negative x plus 8

12 − x = 8
12 minus x equals 8

12 − x = −8
12 minus x equals negative 8
Question 4
A)What is the first step in solving the equation 12(x + 7) = 0 for x?(1 point)
Responses

Divide both sides by 12.
Divide both sides by 12.

Add 7 to both sides.
Add 7 to both sides.

Subtract 7 from both sides.
Subtract 7 from both sides.

Multiply both sides by 12.
Multiply both sides by 12.
Question 5
A)What is the solution to the equation 0.24(x−10.2)=6 when solving for x?(1 point)
Responses

16.44
16.44

14.8
14.8

35.2
35.2

11.64
11.64
Question 6
A)Solve for x in the equation 811(x+45)=2455.(1 point)
$$
Question 7
A)What is the solution to the equation 1.26(x−7.352)=6.426 when solving for x?(1 point)
Responses

12.452
12.452

15.038
15.038

−2.252
negative 2.252

15.44876
15.44876
Question 8
A)Solve for x in the equation −6.29(x+7.85)=−19.499.(1 point)
$$
Question 9
A)Bags of clementines have 12 each. For a party, Sal, Trisha, and Joe each brought bags of clementines. Altogether, there were 180 clementines. Sal brought 4 bags and Joe brought 6. Write the equation to determine how many bags Trisha brought, t.(2 points)
$$(t+$$) = $$
Question 10
A)Dahlia bought Granny Smith and Macintosh apples at the grocery store. The Granny Smith apples were $1.35 each if you bought 6. Find the cost of each Macintosh apple if the total cost is $15 and she bought 6 of each.(1 point)
Each Macintosh apple cost $$$.
Question 11
A)Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1 more than the guitar picks. He spent a total of $40. If c is the cost of one guitar pick, find the cost of one guitar string.(1 point)
$$$
Question 12
A)Fill in the spaces to solve each step of the problem 14(x+3)=5.(2 points)
Step 1: ($$)14(x+3)=5($$).
Step 2: x+3= $$.
Step 3: Subtract $$ from both sides.
Step 4: x= $$
Question 13
A)Marbles come in two sizes: 1-inch diameter and 2-inch diameter. The 1-inch diameter marbles cost 30 cents less than the 2-inch marbles. Rochelle buys 25 1-inch marbles for her science project and spends exactly $10. Find the cost of a 2-inch marble.(1 point)
Responses

$2.50
$2.50

$0.10
$0.10

$2.80
$2.80

$0.70
$0.70
Question 14
A)A local dumpling shop sold 85,248 dumplings last year. Each plate of dumplings sells for $9.89, and there are 12 dumplings per plate. Which value best estimates the shop’s total earnings from selling dumplings?(1 point)
Responses

8,000,000
8,000,000

8,000
8,000

80,000
80,000

800,000
800,000
Question 15
A)Tickets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, what is the regular price of each ticket? Write and solve an equation of the form p(x±q)=r. Then write a sentence to explain your answer.(4 points)

1 answer

Let's address each question one by one with answers and explanations as needed:

Question 1

First Step in Solving 20 = 6x - 4:

  • Correct Response: Add 4 to both sides.

Question 2

Shawnece Multiplying Both Sides by 7:

  • Correct Response: Multiplying both sides by 7 undoes the division of x by 7 in the original problem.

Question 3

Tillie's First Step in Solving:

  • Correct Response: 12 = −x + 8

Question 4

First Step in Solving 12(x + 7) = 0:

  • Correct Response: Divide both sides by 12.

Question 5

Solution to 0.24(x−10.2)=6:

  1. First, divide by 0.24: x - 10.2 = 6 / 0.24
  2. Then solve for x:
    • x - 10.2 = 25
    • x = 25 + 10.2 = 35.2
  • Correct Response: 35.2

Question 6

Solve for x in 811(x + 45) = 2455:

  1. Divide both sides by 811: \[ x + 45 = \frac{2455}{811} = 3.0256 \]
  2. Then subtract 45: \[ x = 3.0256 - 45 \approx -41.9744 \]

Question 7

Solution to 1.26(x - 7.352) = 6.426:

  1. Divide both sides by 1.26: \[ x - 7.352 = \frac{6.426}{1.26} = 5.1 \]
  2. Then solve for x: \[ x = 5.1 + 7.352 = 12.452 \]
  • Correct Response: 12.452

Question 8

Solve for x in −6.29(x + 7.85) = −19.499:

  1. Divide both sides by -6.29: \[ x + 7.85 = \frac{-19.499}{-6.29} \approx 3.099 \]
  2. Then subtract 7.85: \[ x = 3.099 - 7.85 \approx -4.751 \]

Question 9

Equation for how many bags Trisha brought:

  • Response: (t + 4 + 6) = 15
  • Simplified: (t + 10) = 15

Question 10

Cost of Each Macintosh Apple:

  1. Cost for Granny Smith: \(6 \times 1.35 = 8.10\)
  2. Total cost is 15, so: \[ 15 - 8.10 = 6.90 \]
  3. Cost for Macintosh apples (6 apples): \[ \text{Cost of each = } \frac{6.90}{6} = 1.15 \]
  • Each Macintosh apple cost: $1.15.

Question 11

Cost of One Guitar String:

  1. Let c = cost of one guitar pick. Hence, cost of one guitar string is \(c + 1\).
  2. Total cost: \[ 25c + 25(c + 1) = 40 \] Simplifying gives: \[ 50c + 25 = 40 \] \[ 50c = 15 \Rightarrow c = 0.30 \]
  3. Then the cost of one guitar string: \[ 0.30 + 1 = 1.30 \]
  • Answer: $1.30

Question 12

Fill in the steps to solve 14(x + 3) = 5:

  • Step 1: 14(x + 3) = 5.
  • Step 2: x + 3 = 5 / 14.
  • Step 3: Subtract 3 from both sides.
  • Step 4: x = (5/14) - 3.

Question 13

Cost of a 2-inch Marble:

  1. Let the cost of a 2-inch marble = \(x\). So, cost of a 1-inch marble = \(x - 0.30\).
  2. Cost for 25 1-inch marbles: \[ 25(x - 0.30) = 10 \] Thus: \[ 25x - 7.5 = 10 \Rightarrow 25x = 17.5 \Rightarrow x = 0.70 \]
  • Correct Response: $0.70

Question 14

Estimate Total Earnings from Dumplings:

  1. Total dumplings = 85,248
  2. Plates sold = \(85,248 / 12 \approx 7,104\)
  3. Total earnings = \(7,104 \times 9.89 \approx 70,000\)
  • Correct Response: 800,000 (best estimate).

Question 15

Regular Price of Each Ticket:

  1. Let \(p\) be the regular price. Sale price = \(p - 1.50\).
  2. Equation from total cost: \[ 6(p - 1.50) = 51 \] Solving: \[ 6p - 9 = 51 \Rightarrow 6p = 60 \Rightarrow p = 10 \]
  • Sentence Explanation: The regular price of each ticket is $10.