Hank's work to solve the equation 25= x/4 - 9 is shown. In which step did Hank make a mistake, and what mistake did he make?

Step 1:
16 = x/4

Step 2:
x = 64

1 answer

Hank made a mistake in Step 1 of his work.

The original equation is:

\[ 25 = \frac{x}{4} - 9 \]

To isolate \(\frac{x}{4}\), you need to add 9 to both sides:

\[ 25 + 9 = \frac{x}{4} \] \[ 34 = \frac{x}{4} \]

So the correct equation should be:

\[ 34 = \frac{x}{4} \]

Hank incorrectly wrote this as \(16 = \frac{x}{4}\) in Step 1.

Thus, the mistake is that he miscalculated the left side of the equation after adding 9 and incorrectly resulted in \(16\) instead of \(34\).

Then, in Step 2, Hank similarly made an error based on his incorrect Step 1 when he multiplied both sides by 4 to find \(x\):

With the incorrect equation \(16 = \frac{x}{4}\), multiplying both sides by 4 gives:

\[ x = 64 \]

However, the correct calculation using \(34 = \frac{x}{4}\) would give:

\[ x = 34 \times 4 = 136 \]

So, the correct value of \(x\) should be 136, not 64.