Answer
$z=-\frac{1}{2}$
Work Step by Step
We are given that $\frac{2z+7}{8}-2=z+\frac{z-1}{2}$. First, we can multiply each term by 8. Since this is the least common denominator of each term, this will eliminate all fractions from the equation.
$\frac{2z+7}{8}\times8-2\times8=z\times8+\frac{z-1}{2}\times8$
$2z+7-16=8z+4\times(z-1)$
Use the distributive property to simplify the right side.
$2z+7-16=8z+4z-4$
Group like terms on both sides.
$2z-9=12z-4$
Add 9 to both sides.
$2z=12z+5$
Subtract 12z from both sides.
$-10z=5$
Divide both sides by -10.
$z=-\frac{1}{2}$
