Identify the first step in solving this equation for x : 7(x − 8) = 49 . (1 point)

Question

Responses

Divide both sides by 7.
Divide both sides by 7.

Multiply both sides by 7.
Multiply both sides by 7.

Divide only the left side by 7.
Divide only the left side by 7.

Add 8 to both sides.
Add 8 to both sides.

Answer 1

The first step in solving the equation \( 7(x - 8) = 49 \) for \( x \) is to divide both sides by 7. This simplifies the equation and allows you to isolate the term containing \( x \).

So the correct response is: Divide both sides by 7.

Answer 2

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

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

Divide both sides by −3
.
Divide both sides by negative 3.

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

Subtract 6 from both sides.

Answer 3

To solve the equation \( -3(y + 6) = 21 \), the first step would typically be to divide both sides by -3, which simplifies to \( y + 6 = -7 \).

Following this, the second step is to subtract 6 from both sides to isolate \( y \).

So the correct response is: Subtract 6 from both sides.

Answer 4

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

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

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

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

Answer 5

To find which equation allows us to first divide both sides by 6 and then add 8 to both sides, we can analyze each equation:

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

   • Dividing by 6: \( x - \frac{8}{6} = 8\)
   • Then adding 8 won't isolate \(x\) nicely in this case.

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

   • Dividing by 8: \(x - 6 = 6\)
   • Then adding 6 would help isolate \(x\), not adding 8.

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

   • Dividing by 6: \(x - 8 = 8\)
   • Then adding 8: \(x = 16\) works.

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

   • Dividing by 6: \(x + 8 = 8\)
   • Adding 8 here also doesn't get us to a useful step to isolate \(x\).

Based on this analysis, the equation that allows you to first divide by 6 and then add 8 to both sides is:

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

Answer 6

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

2x + 10 = 16
2 x plus 10 equals 16

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

2(x − 10) = 16

Answer 7

To find the equation for which the order of steps allows you to first divide both sides by 2 and then subtract 10 from both sides, let's analyze each option:

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

   • Dividing by 2 gives: \(x + 10 = 8\)
   • Subtracting 10 results in \(x = -2\).

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

   • Dividing by 2 gives: \(x + 5 = 8\)
   • Subtracting 10 would not make sense here, as it would lead to a contradiction.

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

   • Dividing by 10 gives: \(x + 2 = 1.6\)
   • Subtracting 10 is not applicable here as it wouldn't isolate \(x\).

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

   • Dividing by 2 gives: \(x - 10 = 8\)
   • Subtracting 10 would not make sense here as it doesn't isolate \(x\) even after that step.

The only equation that allows you to first divide both sides by 2 and then subtract 10 is:

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

Answer 8

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

21
21

−6
negative 6

24
24

−21

Answer 9

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

1. Divide both sides by -4: \[ z + 12 = \frac{36}{-4} \] \[ z + 12 = -9 \]

2. Subtract 12 from both sides: \[ z = -9 - 12 \] \[ z = -21 \]

Thus, the solution for \( z \) is −21.