Question

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

10(x + 2) = 16
10
(
𝑥

+

2
)

=

16
10 Left Parenthesis x plus 2 Right Parenthesis equals 16

2(x − 10) = 16
2
(
𝑥

−

10
)

=

16
2 Left Parenthesis x minus 10 Right Parenthesis equals 16

2(x + 10) = 16
2
(
𝑥

+

10
)

=

16
2 Left Parenthesis x plus 10 Right Parenthesis equals 16

2x + 10 = 16

Answer 1

To find an equation where the steps involve first dividing both sides by 2, and then subtracting 10 from both sides, we can analyze each of the provided options:

1. **10(x + 2) = 16**
- Dividing both sides by 10 would be a step, not 2. So, this equation does not match.

2. **2(x − 10) = 16**
- Dividing by 2 gives: x - 10 = 8. Then, subtracting 10 gives: x = 8 + 10, which solves to x = 18. This equation matches the steps.

3. **2(x + 10) = 16**
- Dividing by 2 gives: x + 10 = 8. Then, subtracting 10 gives: x = 8 - 10, which solves to x = -2. This equation does not match.

4. **2x + 10 = 16**
- Dividing by 2 gives: x + 5 = 8. Then, subtracting 5 gives: x = 8 - 5, which does not match the required steps.

Thus, the only equation that follows the order of steps to first divide both sides by 2 and then subtract 10 from both sides is:

**2(x − 10) = 16**.

Answer 2

What is the solution of the equation −4(z + 12) = 36
−
4
(
𝑧

+

12
)

=

36
when solving for z
𝑧
? (1 point)
Responses

21
21

24
24

−21
−
21
negative 21

−6
−
6
negative 6

Answer 3

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**:
\[
z = -9 - 12
\]
\[
z = -21
\]

So, the solution for \(z\) is \(\textbf{-21}\).