Question

How many solutions does the equation have?

4(z−5)+2=4z−18

Responses

0
0

1
1

infinitely many
infinitely many

Answer 1

To solve the equation \( 4(z - 5) + 2 = 4z - 18 \), we first simplify both sides.

Starting with the left side:
\[
4(z - 5) + 2 = 4z - 20 + 2 = 4z - 18
\]

Now, the equation becomes:
\[
4z - 18 = 4z - 18
\]

Now, we see that both sides of the equation are identical, which means that this equation is true for any value of \( z \).

Thus, the solution is that there are infinitely many solutions.

The correct response is:
**infinitely many**.