Question

Q. 5. Solve the following equation: 10 + x 3=110 + x 3=1 (1 point) Responses x = - 7 x = - 7 x = 33 x = 33 x = -27 x = -27 x = 21
GPT 3.5
To solve the equation, we need to isolate the variable x on one side.

10 + x/3 = 110 + x/3

To remove the fraction, we can multiply every term by 3:

3(10 + x/3) = 3(110 + x/3)

30 + x = 330 + x

Since the x terms are the same on both sides, we can subtract x from both sides:

30 = 330

This is not a solvable equation. Therefore, there is no solution for x in this equation.
Q. 6. Solve the following equation: 7 (3x - 4) = 49(1 point) Responses x = 1 x = 1 x = 2.5 x = 2.5 x = 311311x = 3 over 11 x = 113
GPT 3.5
To solve the equation, we will simplify and isolate the variable x.

Starting with the given equation:
7(3x - 4) = 49

First, distribute 7 to the terms inside the parentheses:
21x - 28 = 49

Next, add 28 to both sides of the equation:
21x = 49 + 28
21x = 77

Finally, divide both sides by 21:
x = 77 / 21
x = 3.666...

So, the solution to the equation is x = 3.666... (which can be approximated as x = 3.67).
Q. 7. Solve the following equation: 1.3 + 0.5x = -3.41(1 point) Responses x = -4.22 x = -4.22 x = -9.42 x = -9.42 x = 4.22 x = 4.22 x = 9.42
GPT 3.5
To solve the equation, we need to isolate the variable x on one side.

1.3 + 0.5x = -3.41

Subtract 1.3 from both sides of the equation:

0.5x = -3.41 - 1.3
0.5x = -4.71

Finally, divide both sides by 0.5:

x = -4.71 / 0.5
x = -9.42

So, the solution to the equation is x = -9.42.
Q. 8. Solve the following equation: (413) x = 9(413) x = 9 (1 point) Responses x = 29.25 x = 29.25 x = 2.77 x = 2.77 x = 8.69 x = 8.69 x = 26.15
GPT 3.5
To solve the equation, we can divide both sides by 413:

(413) x = 9(413)

x = 9

So, the solution to the equation is x = 9.
Solve the following equation: (4/13) x = 9(4/13) x = 9 (1 point) Responses x = 29.25 x = 29.25 x = 2.77 x = 2.77 x = 8.69 x = 8.69 x = 26.15
GPT 3.5
To solve the equation, we can multiply both sides by the reciprocal of (4/13), which is (13/4):

(4/13) x = 9(4/13) x = 9

(13/4)(4/13) x = 9(13/4)

1x = 9(13/4)

Simplifying the right side:

x = (9)(13/4)

x = 117/4

This can also be expressed as a decimal as approximately x = 29.25.

So, the solution to the equation is x = 29.25.
Q. 9. Solve the following equation: 4 (2y + 1) = 2(y - 13)(1 point) Responses y = −73−73y = negative 7 thirds y = 5 y = 5 y = −176−176y = negative 17 sixths y = - 5
GPT 3.5
To solve the equation, we will distribute on the left side of the equation and simplify:

4(2y + 1) = 2(y - 13)

8y + 4 = 2y - 26

Next, move all terms containing y to one side by subtracting 8y from both sides:

8y - 8y + 4 = 2y - 8y - 26

4 = -6y - 26

Next, move the constant term to the other side by adding 26 to both sides:

4 + 26 = -6y - 26 + 26

30 = -6y

Finally, solve for y by dividing both sides by -6:

y = -30 / 6

y = -5

So, the solution to the equation is y = -5.