Answer
$z=0.8$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
0.91-0.2z=1.23-0.6z
,$ remove first the decimal numbers by multiplying both sides by a power of $10.$ Then use the properties of equality to isolate the variable. Do checking of the solution.
$\bf{\text{Solution Details:}}$
Since the largest number of decimal places a term has is $2,$ multiply both sides by $100.$ This results to
\begin{array}{l}\require{cancel}
0.91-0.2z=1.23-0.6z
\\\\
100(0.91-0.2z)=100(1.23-0.6z)
\\\\
91-20z=123-60z
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
91-20z=123-60z
\\\\
-20z+60z=123-91
\\\\
40z=32
\\\\
z=\dfrac{32}{40}
\\\\
z=\dfrac{\cancel8(4)}{\cancel8(5)}
\\\\
z=\dfrac{4}{5}
\\\\
z=0.8
.\end{array}
Checking: If $z=0.8,$ then
\begin{array}{l}\require{cancel}
0.91-0.2z=1.23-0.6z
\\\\
0.91-0.2(0.8)=1.23-0.6(0.8)
\\\\
0.91-0.16=1.23-0.48
\\\\
0.75=0.75
\text{ (TRUE) }
.\end{array}
Hence, the solution is $
z=0.8
.$
