Question

Half the sum of a number and 26 is 15. What is the number?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's represent the number as x.

According to the given condition, the equation that represents the problem is:

(1/2)x + 26 = 15

Subtract 26 from both sides of the equation:

(1/2)x = 15 - 26

Simplify the right side:

(1/2)x = -11

To solve for x, we need to isolate it on one side of the equation. Multiply both sides by 2:

2(1/2)x = -11 * 2

Simplify:

x = -22

Therefore, the number is -22.

Answer 2

Four times the difference of a number and 7 is 12. What is the number?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's represent the number as x.

According to the given condition, the equation that represents the problem is:

4(x - 7) = 12

Expand the equation:

4x - 28 = 12

Add 28 to both sides of the equation:

4x = 12 + 28

Simplify the right side:

4x = 40

To solve for x, we need to isolate it on one side of the equation. Divide both sides by 4:

(4x)/4 = 40/4

Simplify:

x = 10

Therefore, the number is 10.

Answer 4

What is the first step in solving the equation

3=6y+9

Answer 5

[AI-generated answer — Bot GPT 3.5]

The first step in solving the equation 3 = 6y + 9 is to isolate the variable y.

To do this, we can begin by subtracting 9 from both sides of the equation:

3 - 9 = 6y + 9 - 9

This simplifies to:

-6 = 6y

After isolating the variable, we can proceed with solving for y.

Answer 6

Simplify the expression

2(3x+4)-3(2x-2)+8(x-5)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 2(3x + 4) - 3(2x - 2) + 8(x - 5), we can distribute the coefficients:

2(3x + 4) - 3(2x - 2) + 8(x - 5)
= 6x + 8 - 6x + 6 + 8x - 40

Now, we can combine like terms:

= (6x - 6x + 8x) + (8 + 6 - 40)
= 8x + (-26)
= 8x - 26

Therefore, the simplified expression is 8x - 26.

Answer 8

Write an equation and solve: Four times a number, decreased by 4 is 8.

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let's represent the number as x.

The equation that represents the problem is:

4x - 4 = 8

To solve for x, we need to isolate it on one side of the equation.

Add 4 to both sides of the equation:

4x - 4 + 4 = 8 + 4

Simplify:

4x = 12

Now, divide both sides of the equation by 4:

(4x) / 4 = 12 / 4

Simplify:

x = 3

Therefore, the number is 3.

Answer 10

[AI-generated answer — Explain Bot]

To find the number, we can set up an equation using the given information. Let's call the number 'x'.

The first part of the problem states that "half the sum of a number and 26." So, we can write this part as (x + 26) / 2.

The second part of the problem states that "half the sum of a number and 26 is 15." So, we can set up the equation as:

(x + 26) / 2 = 15

To solve for the variable 'x', we can multiply both sides of the equation by 2:

2 * (x + 26) / 2 = 15 * 2

This simplifies to:

x + 26 = 30

To isolate 'x', we can subtract 26 from both sides of the equation:

x = 30 - 26

This simplifies to:

x = 4

Therefore, the number is 4.