Identify the second step in solving this equation for y : −3(y + 6) = 21 . (1 point)

Question

Responses

Subtract 6 from both sides.
Subtract 6 from both sides.

Divide both sides by 6.
Divide both sides by 6.

Add 6 to both sides.
Add 6 to both sides.

Divide both sides by −3.

Answer 1

To solve the equation \(-3(y + 6) = 21\), the first step is to isolate the term containing \(y\) by dividing both sides by \(-3\). This gives us:

\[ y + 6 = -7 \]

The second step, after dividing both sides by \(-3\), is to subtract \(6\) from both sides to solve for \(y\).

Therefore, the correct answer for the second step is:

Subtract 6 from both sides.

Answer 2

For which equation is the order of steps to first divide both sides by 6 and then to add 8 to both sides?(1 point)
Responses

6x − 8 = 48
6 x minus 8 equals 48

6(x + 8) = 48
6 left parenthesis x plus 8 right parenthesis equals 48

6(x − 8) = 48
6 left parenthesis x minus 8 right parenthesis equals 48

8(x − 6) = 48

Answer 3

To find which equation allows for the steps of first dividing both sides by 6 and then adding 8 to both sides, we need to analyze each option.

1. \(6x - 8 = 48\):

   • Dividing both sides by 6 gives \(x - \frac{8}{6} = 8\) (not an integer operation).

2. \(6(x + 8) = 48\):

   • Dividing both sides by 6 gives \(x + 8 = 8\), and then we would subtract 8, not add it.

3. \(6(x - 8) = 48\):

   • Dividing both sides by 6 gives \(x - 8 = 8\), and then we would add 8 to both sides: \(x = 16\).

4. \(8(x - 6) = 48\):

   • Dividing both sides by 8 gives \(x - 6 = 6\), and then we would add 6, not 8.

The correct equation that allows for dividing by 6 first and then adding 8 is:

6(x - 8) = 48

Answer 4

For which equation is the order of steps to first divide both sides by 2 and then to subtract 10 from both sides?(1 point)
Responses

2(x + 10) = 16
2 Left Parenthesis x plus 10 Right Parenthesis equals 16

2(x − 10) = 16
2 Left Parenthesis x minus 10 Right Parenthesis equals 16

10(x + 2) = 16
10 Left Parenthesis x plus 2 Right Parenthesis equals 16

2x + 10 = 16

Answer 5

To identify which equation allows for the steps of first dividing both sides by 2 and then subtracting 10 from both sides, let's analyze each option:

1. \(2(x + 10) = 16\):

   • Dividing both sides by 2 gives \(x + 10 = 8\). Then, if you subtract 10, you'd get \(x = -2\).

2. \(2(x - 10) = 16\):

   • Dividing both sides by 2 gives \(x - 10 = 8\). If you then add 10, you'd get \(x = 18\) (not subtracting).

3. \(10(x + 2) = 16\):

   • Dividing both sides by 10 gives \(x + 2 = 1.6\). If you then subtract 2, you'd get \(x = -0.4\) (not subtracting 10).

4. \(2x + 10 = 16\):

   • To isolate \(x\), you would first subtract 10, giving \(2x = 6\), and then divide by 2.

The only equation that allows for first dividing by 2 and then subtracting 10 from both sides is:

\(2(x + 10) = 16\).

Answer 6

What is the solution of the equation  −4(z + 12) = 36 when solving for z ? (1 point)
Responses

24
24

−6
negative 6

−21
negative 21

21

Answer 7

To solve the equation \(-4(z + 12) = 36\) for \(z\), we can follow these steps:

1. Divide both sides by -4 to isolate the expression in parentheses: \[ z + 12 = \frac{36}{-4} \] \[ z + 12 = -9 \]

2. Subtract 12 from both sides to solve for \(z\): \[ z = -9 - 12 \] \[ z = -21 \]

So, the solution for the equation is:

−21.