Is \( \frac{1}{2} \) a solution to the equation \( 2 x-8=-7 ? \) Why or why not?

Yes, \( \frac{1}{2} \) is a solution to the equation \( 2x - 8 = -7 \). Here's why: ### Step-by-Step Verification 1. **Start with the original equation:** \[ 2x - 8 = -7 \] 2. **Substitute \( x = \frac{1}{2} \) into the equation:** \[ 2\left(\frac{1}{2}\right) - 8 = -7 \] 3. **Perform the multiplication:** \[ 1 - 8 = -7 \] 4. **Simplify the left side:** \[ -7 = -7 \] Since both sides of the equation are equal after substitution, \( \frac{1}{2} \) satisfies the equation. Therefore, \( \frac{1}{2} \) **is** a solution to \( 2x - 8 = -7 \). ### Additional Confirmation If you prefer solving the equation to find the value of \( x \), here's how you can do it: 1. **Start with the equation:** \[ 2x - 8 = -7 \] 2. **Add 8 to both sides to isolate the term with \( x \):** \[ 2x = -7 + 8 \] \[ 2x = 1 \] 3. **Divide both sides by 2 to solve for \( x \):** \[ x = \frac{1}{2} \] This confirms that \( x = \frac{1}{2} \) is indeed the solution to the equation.