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The length of a rectangle is four meters less than twice its width. If the area of the rectangle is 96 m^2, what is the length and the width? (3 points)

An expression for the length of the rectangle in terms of the width would be: ______

The formula for the area of a rectangle is: ______

Using trial and error, if the area is 96 m^2, then the length and width are: _____
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Match the equation with its solution(s).(5 points)

3(2i+7)=61+21
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3(2i+7)=6i+21
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3i+5=2i-7
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3(2i-7)=15
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3i+5=3i+7
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3i+2i-7=18
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Solve the equation justifying each step with the correct reasoning.

2(x+8)=2x+8
(5 points)
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Match the description of the one variable equation with the number of solutions it will have.(4 points)

A: x−7=7−x =

B: 3(x+5)=3x+5 =

C: 10−x=25 =

D: 2(x+4)=2x+5+3 =
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A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.

Let n represent the number of notebooks that he buys.

Which inequality describes this scenario?

(1 point)
Answer
A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.

Let n represent the number of notebooks that he buys.

Which inequality describes this scenario?

(1 point)
Responses

37 > 2n + 24
24n + 2 ≥ 37
37 ≥ 2n + 24
37 < 2n + 24
Answer
did this give u a good grade?
Answered by GPT 3.5
An expression for the length of the rectangle in terms of the width would be: 2w - 4

The formula for the area of a rectangle is: length × width

Using trial and error, if the area is 96 m^2, then the length and width are: length = 12 m and width = 8 m
Answered by GPT 3.5
3(2i+7) = 61 + 21

Multiply:

6i + 21 = 82

Subtract 21 from both sides:

6i = 61

Divide by 6:

i = 10.17

The solution is i = 10.17
Answered by GPT 3.5
3(2i+7) = 6i + 21

Distribute:

6i + 21 = 6i + 21

Subtract 6i from both sides:

21 = 21

The equation is true for all values of i. There are infinitely many solutions.
Answered by GPT 3.5
3i + 5 = 2i - 7

Subtract 2i from both sides:

i + 5 = -7

Subtract 5 from both sides:

i = -12

The solution is i = -12.
Answered by GPT 3.5
3(2i - 7) = 15

Distribute:

6i - 21 = 15

Add 21 to both sides:

6i = 36

Divide by 6:

i = 6

The solution is i = 6.
Answered by GPT 3.5
3i + 5 = 3i + 7

Subtract 3i from both sides:

5 = 7

This equation is not possible as 5 does not equal 7. Therefore, there is no solution.
Answered by GPT 3.5
3i + 2i - 7 = 18

Combine like terms:

5i - 7 = 18

Add 7 to both sides:

5i = 25

Divide by 5:

i = 5

The solution is i = 5.
Answered by GPT 3.5
2(x+8) = 2x + 8

Distribute the 2:

2x + 16 = 2x + 8

Subtract 2x from both sides:

16 = 8

This equation is not possible as 16 does not equal 8. Therefore, there is no solution.
Answered by GPT 3.5
A: x-7=7-x - This equation will have one solution.

B: 3(x+5)=3x+5 - This equation will have infinitely many solutions.

C: 10-x=25 - This equation will have one solution.

D: 2(x+4)=2x+5+3 - This equation will have no solutions.
Answered by GPT 3.5
The inequality that describes this scenario is:

2n + 24 ≤ 37
Answered by GPT 3.5
37 ≥ 2n + 24