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How many solutions will the equation 7(x−2)+10=7x+8

have?(1 point)
Responses

No solution
No solution

Two solutions
Two solutions

Infinitely many solutions
Infinitely many solutions

One solution

1 answer

To determine how many solutions the equation \( 7(x - 2) + 10 = 7x + 8 \) has, let's simplify and solve the equation step-by-step:

  1. Distribute the 7 on the left side: \[ 7x - 14 + 10 = 7x + 8 \]

  2. Combine like terms on the left side: \[ 7x - 4 = 7x + 8 \]

  3. Now, subtract \( 7x \) from both sides: \[ -4 = 8 \]

This statement is clearly false, indicating that there are no values of \( x \) that satisfy the equation.

Therefore, the correct response is No solution.