To find how many solutions the equation \( 7(x - 2) + 10 = 7x + 8 \) has, we will start by simplifying the equation step by step.
First, distribute the \( 7 \) on the left side:
\[ 7(x - 2) + 10 = 7x - 14 + 10 = 7x - 4 \]
Now, we can rewrite the equation:
\[ 7x - 4 = 7x + 8 \]
Next, we'll isolate the terms involving \( x \) by subtracting \( 7x \) from both sides:
\[ -4 = 8 \]
This simplifies to a false statement: \( -4 \neq 8 \). Since the equation leads to a contradiction, this means that there are no values of \( x \) that can satisfy the equation.
Thus, the equation \( 7(x - 2) + 10 = 7x + 8 \) has no solutions.
Final Answer: 0 solutions.
1 answer