Question

-2 (4 + n) = 24

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we will first distribute -2 to the terms inside the parentheses.

-2(4 + n) = 24

-8 - 2n = 24

Next, we will isolate the variable by adding 8 to both sides of the equation.

-2n = 24 + 8

-2n = 32

To solve for n, we divide both sides by -2.

n = 32/-2

n = -16

Therefore, the solution to the equation -2(4 + n) = 24 is n = -16.

Answer 2

[AI-generated answer — Explain Bot]

To solve the equation -2(4 + n) = 24, we can follow these steps:

1. Distribute the -2 to the terms inside the parentheses using the distributive property of multiplication.
-2 * 4 + -2 * n = 24

2. Multiply -2 by 4.
-8 + -2 * n = 24

3. Multiply -2 by n.
-8 - 2n = 24

4. Since the equation contains a variable, we want to isolate the variable on one side of the equation. Let's start by moving the constant term to the other side.
-8 - 2n + 8 = 24 + 8

Simplifying, we have:
-2n = 32

5. To solve for n, we can divide both sides of the equation by -2.
-2n / -2 = 32 / -2

Simplifying, we have:
n = -16

Therefore, the solution to the equation -2(4 + n) = 24 is n = -16.

Answer 3

5/8 (x + 1/2) = 100

Answer 4

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we will follow these steps:

1. Distribute 5/8 to the terms inside the parentheses using the distributive property of multiplication.
(5/8) * x + (5/8) * (1/2) = 100

2. Multiply 5/8 by x.
(5/8) * x + 5/16 = 100

3. Simplify the expression 5/8 * x to (5x)/8.
(5x)/8 + 5/16 = 100

4. Now, we want to isolate the variable on one side of the equation. Let's start by moving the constant term to the other side.
(5x)/8 = 100 - 5/16

Simplifying the right side, we have:
(5x)/8 = 1600/16 - 5/16
(5x)/8 = 1595/16

5. To solve for x, we can multiply both sides of the equation by 8/5.
(8/5) * (5x)/8 = (8/5) * (1595/16)

Simplifying, we have:
x = (8 * 1595) / (5 * 16)
x = 12760/80
x = 159.5

Therefore, the solution to the equation 5/8 (x + 1/2) = 100 is x = 159.5.

Answer 5

0.7 (w + 1.2) = 2.1

Answer 6

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we will follow these steps:

1. Distribute 0.7 to the terms inside the parentheses using the distributive property of multiplication.
0.7w + 0.7 * 1.2 = 2.1

2. Multiply 0.7 by 1.2.
0.7w + 0.84 = 2.1

3. Now, we want to isolate the variable on one side of the equation. Let's start by moving the constant term to the other side.
0.7w = 2.1 - 0.84
0.7w = 1.26

4. To solve for w, we divide both sides of the equation by 0.7.
(0.7w)/0.7 = 1.26/0.7

Simplifying, we have:
w = 1.8

Therefore, the solution to the equation 0.7(w + 1.2) = 2.1 is w = 1.8.

Answer 7

-30 (s - 10) = -180

Answer 8

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we will follow these steps:

1. Distribute -30 to the terms inside the parentheses using the distributive property of multiplication.
-30s + 300 = -180

2. Now, we want to isolate the variable on one side of the equation. Let's start by moving the constant term to the other side.
-30s = -180 - 300
-30s = -480

3. To solve for s, we divide both sides of the equation by -30.
(-30s)/(-30) = (-480)/(-30)

Simplifying, we have:
s = 16

Therefore, the solution to the equation -30(s - 10) = -180 is s = 16.

Answer 9

Half the sum of a number and 10 is 8. Find the number

Answer 10

[AI-generated answer — Bot GPT 3.5]

To solve the problem, we can follow these steps:

1. Let's assign a variable to the unknown number. Let's call it "x".

2. The sum of x and 10 is x + 10.

3. Half the sum of the number and 10 is (1/2)(x + 10).

4. We are told that this expression is equal to 8. So, we can set up an equation:
(1/2)(x + 10) = 8

5. To solve for x, we can first remove the fraction by multiplying both sides of the equation by 2:
2 * (1/2)(x + 10) = 2 * 8
x + 10 = 16

6. Next, let's isolate x by subtracting 10 from both sides of the equation:
x + 10 - 10 = 16 - 10
x = 6

Therefore, the number we are looking for is x = 6.

Answer 11

john buys 8 packs of cookies at the grocery store. The cookies are on sale for 50 cents off per pack. He spends $20. Which equation can be used to find the original ost of a box of cookies, c?

Answer 12

[AI-generated answer — Bot GPT 3.5]

Let's assume the original cost of a pack of cookies is c dollars.

Since there are 8 packs of cookies, and each pack is on sale for 50 cents off, the savings per pack would be 0.50 * 8 = 4 dollars.

The amount John spends is $20, which is the total cost after the discount.

The equation that can be used to find the original cost of a pack of cookies, c, is as follows:

8c - 4 = 20

In this equation, 8c represents the cost of 8 packs of cookies before the discount, and subtracting 4 dollars accounts for the discount. The equation is set equal to 20 since that is the total amount spent by John.

Answer 13

john buys 8 packs of cookies at the grocery store. The cookies are on sale for 50 cents off per pack. He spends $20. Which equation can be used to find the original cost of a box of cookies, c?

A. 8(c + 0.50) = 20

B. 8c - 0.50 = 20

C. 8 (c - 0.50) = 20

D. 8 - 0.50c = 20

Answer 14

[AI-generated answer — Bot GPT 3.5]

The correct equation is A. 8(c + 0.50) = 20.

In this equation, c represents the original cost of a pack of cookies. Since there are 8 packs, we multiply c by 8. Adding 0.50 represents the discount per pack. The equation is set equal to 20 since that is the total amount spent by John.

Answer 15

4 (3x - 2) = -24

Answer 16

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we will follow these steps:

1. Distribute 4 to the terms inside the parentheses using the distributive property of multiplication.
12x - 8 = -24

2. Now, we want to isolate the variable on one side of the equation. Let's start by moving the constant term to the other side.
12x = -24 + 8
12x = -16

3. To solve for x, we divide both sides of the equation by 12.
(12x)/12 = (-16)/12

Simplifying, we have:
x = -4/3

Therefore, the solution to the equation 4(3x - 2) = -24 is x = -4/3.