Question

Hill is solving an equation for x. His second step is to divide both sides of the equation by 5. Which equation is he solving?

7 - z/5 = 22

7 - 5x = 22

7 + z/5 = 22

7 + 5x = 22

Answer 1

To determine which equation Hill is solving, we can analyze each option to see which one, when undergoing the second step of dividing both sides by 5, makes sense:

1. **7 - z/5 = 22**:
- If we were to divide both sides by 5, we'd get:
\[
\frac{7 - z/5}{5} = \frac{22}{5}
\]
- This is not directly useful since the equation involves both addition and subtraction of z/5, and it does not simplify the variable.

2. **7 - 5x = 22**:
- Dividing both sides by 5 gives:
\[
\frac{7 - 5x}{5} = \frac{22}{5}
\]
- This doesn't isolate x in a straightforward manner.

3. **7 + z/5 = 22**:
- Dividing both sides by 5 gives:
\[
\frac{7 + z/5}{5} = \frac{22}{5}
\]
- This will not yield an obvious simplification for z.

4. **7 + 5x = 22**:
- Dividing both sides by 5 gives:
\[
\frac{7 + 5x}{5} = \frac{22}{5}
\]
- This rearranges to:
\[
\frac{7}{5} + x = \frac{22}{5}
\]
- This effectively isolates x in the equation allowing for further steps.

From this analysis, it appears that the most straightforward equation that Hill is likely solving is **7 + 5x = 22** because dividing both sides by 5 leads to a simpler expression that can be further manipulated.