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QuestionSolve the equation 18(z−3)=12(z+12)\frac{1}{8}(z-3)=\frac{1}{2}\left(z+\frac{1}{2}\right) and simplify to an integer, fraction, or decimal.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 18(z−3)=1(z+1)\frac{1}{8}(z-3)=\frac{1}{}\left(z+\frac{1}{}\right). We need to solve for zz
3. We can use the properties of equality to solve the equation

STEP 2

First, we need to distribute the fractions on both sides of the equation.
18z−8=12z+14\frac{1}{8}z - \frac{}{8} = \frac{1}{2}z + \frac{1}{4}

STEP 3

Next, we need to isolate zz on one side of the equation. To do this, we can subtract 18z\frac{1}{8}z from both sides of the equation.
−38=12z−18z+1-\frac{3}{8} = \frac{1}{2}z - \frac{1}{8}z + \frac{1}{}

STEP 4

implify the right side of the equation.
−38=38z+14-\frac{3}{8} = \frac{3}{8}z + \frac{1}{4}

STEP 5

Next, subtract 14\frac{1}{4} from both sides of the equation to isolate zz.
−38−14=38z-\frac{3}{8} - \frac{1}{4} = \frac{3}{8}z

STEP 6

implify the left side of the equation.
−58=38z-\frac{5}{8} = \frac{3}{8}z

STEP 7

Finally, divide both sides of the equation by 3\frac{3}{} to solve for zz.
z=−53z = \frac{-\frac{5}{}}{\frac{3}{}}

STEP 8

implify the right side of the equation.
z=−53z = -\frac{5}{3}So, the solution to the equation 18(z−3)=12(z+12)\frac{1}{8}(z-3)=\frac{1}{2}\left(z+\frac{1}{2}\right) is z=−53z = -\frac{5}{3}.

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