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

1 answer

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.