Question

Solve the equation.

4 – t = 3(t – 1) – 5
(1 point)
Responses

3

6

no solution

identity

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we can start by simplifying both sides:

4 - t = 3(t - 1) - 5

4 - t = 3t - 3 - 5

Next, we can combine like terms:

4 - t = 3t - 8

Rearranging the terms:

4 + 8 = 3t + t

12 = 4t

Finally, divide both sides by 4 to solve for t:

12/4 = t

t = 3

Therefore, the solution to the equation is t = 3.

Answer 2

8x – 2(x + 1) = 2(3x – 1)

(1 point)
Responses

0

2

no solution

identity

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we can start by distributing the terms on both sides:

8x - 2(x + 1) = 2(3x - 1)

8x - 2x - 2 = 6x - 2

Next, we can combine like terms:

6x - 2 = 6x - 2

At this point, we realize that the equation ends up being an identity. This means that any value of x will satisfy the equation. Therefore, the solution is an identity.

Answer 4

3(c – 2) = 2(c – 6)

(1 point)
Responses

2

−6

no solution

identity

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we can start by distributing the terms on both sides:

3(c - 2) = 2(c - 6)

3c - 6 = 2c - 12

Next, we can combine like terms:

3c - 2c = -12 + 6

c = -6

Therefore, the solution to the equation is c = -6.

Answer 6

0.5(m + 4) = 3(m – 1)

(1 point)
Responses

–2

2

no solution

identity

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we can start by distributing the terms on both sides:

0.5(m + 4) = 3(m - 1)

0.5m + 2 = 3m - 3

Next, we can combine like terms:

0.5m - 3m = -2 - 3

-2.5m = -5

To isolate m, we divide both sides by -2.5:

m = -5 / -2.5

m = 2

Therefore, the solution to the equation is m = 2.

Answer 8

The steps for solving the equation 3x + 13 = x + 27 are shown below. What property justifies the second step in the solution?

Answer 9

[AI-generated answer — Bot GPT 3.5]

Unfortunately, the steps for solving the equation are not provided.

Answer 10

Rick is going to buy donuts for his family. Each donut costs $1.25. If the number of donuts Rick buys is represented using the letter r, which expression represents the total cost?

Responses

r1.25

1.25 + r

r - 1.25

1.25r

Answer 11

[AI-generated answer — Bot GPT 3.5]

The correct expression that represents the total cost of the donuts Rick buys is 1.25r.

Answer 12

Which list of numbers contains ONLY integers?

Responses

π, 57 , 8

−5, 0, 4√

−5.3 , 0, 4√

−60√,−83, 2π

Answer 13

[AI-generated answer — Bot GPT 3.5]

The list of numbers that contains ONLY integers is:

−5, 0, 4√

Answer 14

Simplify:

-4(2x + 5)?

Responses

-8x + 20

-2x + 1

-8x - 20

-2x -20

Answer 15

[AI-generated answer — Bot GPT 3.5]

To simplify -4(2x + 5), we distribute the -4 to both terms inside the parentheses:

-4 * 2x + (-4) * 5

Which simplifies to:

-8x - 20

Therefore, the simplified form is -8x - 20.

Answer 16

√62 is between which two integers on the number line?

Responses

61 & 63

31 & 32

7 & 8

8 & 9

Answer 17

[AI-generated answer — Bot GPT 3.5]

To determine which two integers √62 is between on the number line, we can find the two integers between which the square root of 62 lies.

√62 is between 7 and 8.

Therefore, √62 is between 7 and 8 on the number line.

Answer 18

Solve:

15= x+2/−3
Responses

x=−7

x=−47

x=−36

x=−39

Answer 19

[AI-generated answer — Bot GPT 3.5]

To solve the equation 15 = (x + 2) / (-3), we can begin by multiplying both sides of the equation by -3 to eliminate the denominator:

15 * (-3) = (x + 2)

-45 = x + 2

Next, we can isolate x by subtracting 2 from both sides:

-45 - 2 = x

x = -47

Therefore, the solution to the equation is x = -47.

Answer 20

Solve:

−4x+11=41
Responses

x=−15/2

x= −15

x=2

x=15/2

Answer 21

[AI-generated answer — Bot GPT 3.5]

To solve the equation -4x + 11 = 41, we can start by subtracting 11 from both sides:

-4x + 11 - 11 = 41 - 11

-4x = 30

Next, we can isolate x by dividing both sides by -4:

(-4x)/(-4) = 30/(-4)

x = -15/2

Therefore, the solution to the equation is x = -15/2.

Answer 22

What is the first step in solving the equation for y?

3y+12=18
Responses

Divide both sides of the equation by 12.

Subtract 18 from both sides of the equation.

Subtract 12 from both sides of the equation.

Add 3 to both sides of the equation.

Answer 23

[AI-generated answer — Bot GPT 3.5]

To solve the equation 3y + 12 = 18, the first step would be to subtract 12 from both sides of the equation.

Therefore, the correct answer is: Subtract 12 from both sides of the equation.

Answer 24

Solve:14=−13+9x

Responses

x=13

x=−9

x=−3

x=3

Answer 25

[AI-generated answer — Bot GPT 3.5]

To solve the equation 14 = -13 + 9x, we can begin by isolating the variable x.

First, we can add 13 to both sides of the equation:

14 + 13 = -13 + 9x + 13

27 = 9x

Next, we divide both sides of the equation by 9 to solve for x:

27/9 = 9x/9

3 = x

Therefore, the solution to the equation is x = 3.

Answer 26

A rectangle has a length of 14 meters and a width of 25 meters. What is the perimeter of the rectangle?

Responses

50 m

39 m

28 m

78 m

Answer 27

[AI-generated answer — Bot GPT 3.5]

To find the perimeter of a rectangle, we add up all the sides. In this case, the length of the rectangle is 14 meters and the width is 25 meters.

Perimeter = 2(length + width)
Perimeter = 2(14 + 25)
Perimeter = 2(39)
Perimeter = 78 meters

Therefore, the perimeter of the rectangle is 78 meters.

Answer 28

For what value of x is the equation 34+x4=1

true?
Responses

x=1

x=−1

x=7

x=−7

Answer 29

[AI-generated answer — Bot GPT 3.5]

To find the value of x that makes the equation 34 + x/4 = 1 true, we can begin by subtracting 34 from both sides:

34 + x/4 - 34 = 1 - 34

x/4 = -33

Next, we can multiply both sides by 4 to isolate x:

4 * (x/4) = -33 * 4

x = -132

Therefore, the value of x that makes the equation true is x = -132.

Answer 30

For what value of x is the equation 3/4+x/4=1

true?
Responses

x=1

x=−1

x=7

x=−7

Answer 31

[AI-generated answer — Bot GPT 3.5]

To find the value of x that makes the equation 3/4 + x/4 = 1 true, we can begin by subtracting 3/4 from both sides:

3/4 + x/4 - 3/4 = 1 - 3/4

x/4 = 1/4

Next, we can multiply both sides by 4 to isolate x:

4 * (x/4) = 4 * (1/4)

x = 1

Therefore, the value of x that makes the equation true is x = 1.