2. Simplify. Please be sure to show all of your work.

-3(-9) – |-5 – 3

3. Simplify. Please show all of your work
9c^3+7c-(3c^3-12+c)

4. Solve 4x- 3(5x-8) =23-9(x+2) . Please show all of your work

5. Solve the following equation for z. Please show all of your work.
x=1/25(22z-9w)

6. Solve -14x -7(4-7) <(2x-15) . Write your solution using set builder notation. Please show all of your work
7.
Solve. Please show all of your work.
During one year, the Hills' real estate bill included $413 for miscellaneous services. Of this amount, 8% went to the local homeless shelter. How much money did the homeless shelter receive?

8. Solve. Please show all of your work.
Find the length and width of a rectangular lot with a perimeter of 108 meters if the length is 8 meters more than the width.

9. 9. Solve. Please show the algebraic inequality you used and show all of your work.
The Lido Company rents copy machines for a monthly charge of $300 + 10 cents per copy. The Lumsden Company rents copy machines for a monthly charge of $500 + 3 cents per copy. How many copies make the Lido Company more expensive than the Lumsden Company?

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2. I'm assuming you meant:

-3(-9) - [-5-3] =
27 - 8 = 19.

3. 9c^3 + 7c -(3c^3-12+c) =
9c^3 + 7c - 3c^3 + 12 - c =
6c^3 + 6c + 12 =
6(c^3 + c + 2).

4. Similar to # 3.

5. x = 1/25(22x - 9w) =
Multiply both sides by 25:
25x = 22x - 9w,
25x - 22x = 9w,
3x = 9w,
X = 3w.

6. -14x - 7(4-7) < (2x-15)
-14x + 21 < 2x-15
-14x - 2x < -15 - 21,
-16x < -36,
X > -36/-16,
X > 2 1/4.

7. 0.08 * $413 = $33.04

8. Width = X-Met3rs.

Length = (x+8) Meters.

2x + 2(x+8) = 108m.
2x + 2x + 16 = 108,
4x = 108 - 16 = 92,
X = 23m = Width.

X+ 8 = 31m = Length.

9. 0.1x + 300 > 0.03x + 500,
0.1x - 0.03x > 500 - 300,
0.07x > 200,
X > 2857 Copies.

2. To simplify -3(-9) – |-5 – 3|, we can follow the order of operations (PEMDAS/BODMAS).

First, simplify -3(-9) by multiplying -3 with -9.
-3(-9) = 27

Next, simplify |-5 – 3| by subtracting 3 from -5, then taking the absolute value of the result.
|-5 – 3| = |-8| = 8

Finally, subtract the result of the absolute value from the first step.
27 - 8 = 19

So, the simplified answer is 19.

3. To simplify 9c^3+7c-(3c^3-12+c), we can combine like terms.

First, distribute the negative sign to simplify -(3c^3-12+c) as -3c^3 + 12 - c.

Next, combine the like terms.

9c^3 - 3c^3 = 6c^3
7c - c = 6c
12 - 0 = 12

Finally, combine all terms together.
6c^3 + 6c + 12

So, the simplified answer is 6c^3 + 6c + 12.

4. To solve 4x - 3(5x - 8) = 23 - 9(x + 2), we need to simplify and combine like terms.

First, distribute the -3 to simplify -3(5x - 8) as -15x + 24.

Next, distribute the -9 to simplify -9(x + 2) as -9x - 18.

Now, simplify the left side of the equation further.

4x - 15x + 24 = 23 - 9x - 18

Combine like terms on both sides of the equation.

-11x + 24 = 5 - 9x

To isolate the x terms on one side of the equation, subtract -9x from both sides.

-11x + 9x + 24 = 5 - 9x + 9x

Simplify.

-2x + 24 = 5

Next, subtract 24 from both sides to isolate the variable.

-2x = 5 - 24

Simplify further.

-2x = -19

Finally, divide both sides of the equation by -2 to solve for x.

x = -19 / -2

Simplify the answer.

x = 19/2 or x = 9.5

So, the solution is x = 9.5.

5. To solve the equation x = 1/25(22z - 9w) for z, we can follow the steps below.

First, we can distribute 1/25 to simplify the expression.

x = (1/25)*(22z - 9w)

Next, we can simplify further by multiplying 1/25 with each term inside the parentheses.

x = (22z/25) - (9w/25)

To solve for z, we need to isolate the term containing z. So, we move the - (9w/25) term to the other side of the equation by adding it to both sides.

x + (9w/25) = (22z/25)

To get rid of the fraction, we can multiply both sides of the equation by 25.

25(x + (9w/25)) = 25(22z/25)

Simplify.

25x + 9w = 22z

Finally, divide both sides of the equation by 22 to solve for z.

(25x + 9w)/22 = z

So, z = (25x + 9w)/22.

6. To solve -14x - 7(4-7) < (2x-15), we can follow these steps:

First, simplify the expression within parentheses.

-14x - 7(-3) < 2x - 15

Next, simplify further.

-14x + 21 < 2x - 15

To solve for x, we need to isolate the variable. Let's start by moving all terms containing x to one side of the inequality by adding 14x to both sides and subtracting 2x from both sides.

-14x + 14x + 21 + 15 < 2x - 2x - 15 + 15

This simplifies to:

36 < 0

However, this inequality is not possible since 36 is not less than 0. Therefore, there is no solution to this inequality.

7. To find out how much money the local homeless shelter received from the Hills' real estate bill, we can solve the problem using percentages.

The problem states that the homeless shelter received 8% of the total real estate bill, which was $413. To find out how much money the shelter received, we can multiply $413 by 8% (or 0.08).

Amount received by the shelter = $413 * 0.08

Solving this multiplication gives us the answer:

Amount received by the shelter = $33.04

Therefore, the homeless shelter received $33.04 from the Hills' real estate bill.

8. To find the length and width of a rectangular lot with a perimeter of 108 meters, where the length is 8 meters more than the width, let's set up the equation.

Let the width of the lot be represented by W.

Given that the length is 8 meters more than the width, we can represent the length as W + 8.

The perimeter of a rectangle is given by the formula: 2 * (length + width).

According to the problem, the perimeter is 108 meters. So we can set up the equation as:

2 * (W + (W + 8)) = 108

Now, simplify the equation:

2 * (2W + 8) = 108

Multiply:

4W + 16 = 108

Subtract 16 from both sides:

4W = 92

Divide by 4:

W = 23

So the width of the lot is 23 meters.

To find the length, we can substitute the value we found for W into the equation for the length:

Length = Width + 8

Length = 23 + 8 = 31

So the length of the lot is 31 meters.

Therefore, the rectangular lot has a length of 31 meters and a width of 23 meters.

9. To determine how many copies make the Lido Company more expensive than the Lumsden Company, we need to set up an inequality based on the monthly charges.

Let x represent the number of copies made. The Lido Company's monthly charge can be represented as $300 + 0.10x, and the Lumsden Company's monthly charge can be represented as $500 + 0.03x.

We want to find the point where the Lido Company becomes more expensive than the Lumsden Company, which means their total charges are equal.

So we can set up the inequality:

300 + 0.10x > 500 + 0.03x

Next, we can subtract 300 and 0.03x from both sides to isolate the x term.

0.07x > 200

To solve for x, we divide both sides by 0.07:

x > 200 / 0.07

Simplify:

x > 2857.14

Since we can't have a fractional number of copies, we can round up to the nearest whole number.

Therefore, the Lido Company becomes more expensive than the Lumsden Company when the number of copies exceeds 2858.