Question

ow many solutions will the equation 7(x−2)+10=7x+8
have?(1 point)
Responses

One solution
One solution

No solution
No solution

Infinitely many solutions
Infinitely many solutions

Two solutions

Answer 1

To find the number of solutions for the equation \( 7(x - 2) + 10 = 7x + 8 \), we can start by simplifying both sides of the equation:

1. Distribute \( 7 \) on the left side:
\[
7x - 14 + 10 = 7x + 8
\]
Simplifying this gives:
\[
7x - 4 = 7x + 8
\]

2. Next, we can subtract \( 7x \) from both sides:
\[
-4 = 8
\]

This is a false statement. Therefore, the original equation does not hold true for any value of \( x \).

Thus, the answer is **No solution**.