Question

What are the next steps in solving this equation: 4/5 x - 4 = -40
Step 1: 4/5x = -36
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1 point
Multiply by 5 and divide by 4
Multiply by 4 and divide by 5
Subtract 4 and Add 5
Subtract 5 and Add 4
Multiply by 4 and Multiply by 5
Each crate has the same number of rocks

What equation is represented by this balance scale? How many rocks are in each crate?
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1 point
12x + 2 = 3x; there are 2 rocks in each crate
5x + 12 = 3x; there are 6 rocks in each crate
2x + 12 = 3; there are 4 rocks in each crate
2x + 12 = 3x; there are 12 rocks in each crate
What property would you use to get to each step?
Original Equation: -4(x + 3) + 2x = 40
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4 points
Addition Property of Equality Distributive Property Combine like terms Division Property of Equality
Step 1: -4x - 12 + 2x = 40
Step 2: -2x - 12 = 40
Step 3: -2x = 52
Step 4: x = -26
Step 1: -4x - 12 + 2x = 40
Step 2: -2x - 12 = 40
Step 3: -2x = 52
Step 4: x = -26
Each student who buys a school lunch pays $2.75.

The cafeteria typically brings in between $1,168.75 and $1,438.25 each day. How many lunches do they sell each day?

Put the number of lunches the cafeteria could sell on the number line.

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1 point

350 < n <= 650

425 <= n <= 523

475 <= n <= 750

375 < n < 525
Find the mistakes.
5(1 + 4x) + 2x = 27 - x
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5 points
Mistake in this step No Mistake in this step
Step 1: Distribute; 5 + 4x + 2x = 27 - x
Step 2: Combine like terms; 5 + 6x = 27 - x
Step 3: Get x's on one side: 5 - 7x = 27
Step 4: -7x = 22
Step 5: x = 22/-7
Step 1: Distribute; 5 + 4x + 2x = 27 - x
Step 2: Combine like terms; 5 + 6x = 27 - x
Step 3: Get x's on one side: 5 - 7x = 27
Step 4: -7x = 22
Step 5: x = 22/-7

Answer 1

Here are the answers with brief explanations.

1) Solve 4/5 x - 4 = -40. After Step 1: 4/5 x = -36
- Correct choice: Multiply by 5 and divide by 4 (equivalently multiply both sides by 5/4). This gives x = (-36) * (5/4) = -45.

2) Balance-scale problem (each crate has same number of rocks)
- Correct choice: 2x + 12 = 3x; there are 12 rocks in each crate.
(2x + 12 = 3x → 12 = x)

3) Properties used for each step of -4(x + 3) + 2x = 40
- Step 1: -4x - 12 + 2x = 40 → Distributive Property
- Step 2: -2x - 12 = 40 → Combine like terms
- Step 3: -2x = 52 → Addition Property of Equality (added 12 to both sides)
- Step 4: x = -26 → Division Property of Equality (divide both sides by -2)

4) Number of lunches n, given $2.75 each and total between $1,168.75 and $1,438.25
- Correct interval: 425 <= n <= 523
(1168.75/2.75 = 425 and 1438.25/2.75 = 523)

5) Find the mistakes in solving 5(1 + 4x) + 2x = 27 - x
- Step 1: Distribute; 5 + 4x + 2x = 27 - x → Mistake (5*(1+4x) = 5 + 20x, not 5 + 4x)
- Step 2: Combine like terms; 5 + 6x = 27 - x → No mistake (combining 4x + 2x → 6x is correct given Step 1, though Step 1 was wrong)
- Step 3: Get x's on one side: 5 - 7x = 27 → Mistake (should be 5 + 7x = 27)
- Step 4: -7x = 22 → No mistake (correctly follows from the incorrect Step 3)
- Step 5: x = 22/-7 → No mistake (equivalent to x = -22/7)

If you want, I can also show the correct solution for problem 5: starting correctly,
5 + 20x + 2x = 27 - x → 5 + 22x = 27 - x → 23x = 22 → x = 22/23.