Solve 45.5=1/2(8+z)7

$$45.5= \frac{ 1 }{ 2 } (8+z)7$$

Solve for z

$$z=5$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} and 7 to get \frac{7}{2}.

$$45.5=\frac{7}{2}\left(8+z\right)$$

Use the distributive property to multiply \frac{7}{2} by 8+z.

$$45.5=\frac{7}{2}\times 8+\frac{7}{2}z$$

Express \frac{7}{2}\times 8 as a single fraction.

$$45.5=\frac{7\times 8}{2}+\frac{7}{2}z$$

Multiply 7 and 8 to get 56.

$$45.5=\frac{56}{2}+\frac{7}{2}z$$

Divide 56 by 2 to get 28.

$$45.5=28+\frac{7}{2}z$$

Swap sides so that all variable terms are on the left hand side.

$$28+\frac{7}{2}z=45.5$$

Subtract 28 from both sides.

$$\frac{7}{2}z=45.5-28$$

Subtract 28 from 45.5 to get 17.5.

$$\frac{7}{2}z=17.5$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.

$$z=17.5\times \frac{2}{7}$$

Convert decimal number 17.5 to fraction \frac{175}{10}. Reduce the fraction \frac{175}{10} to lowest terms by extracting and canceling out 5.

$$z=\frac{35}{2}\times \frac{2}{7}$$

Multiply \frac{35}{2} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$z=\frac{35\times 2}{2\times 7}$$

Cancel out 2 in both numerator and denominator.

$$z=\frac{35}{7}$$

Divide 35 by 7 to get 5.

$$z=5$$