Answer
$x=\dfrac{3}{5}$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given equation, $
8(x-1)-3(x-2)=1
,$ is equivalent to
\begin{align*}\require{cancel}
8(x)+8(-1)-3(x)-3(-2)&=1
\\
8x-8-3x+6&=1
\\
(8x-3x)+(-8+6)&=1
&(\text{combine like terms})
\\
5x-2&=1
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
5x-2+2&=1+2
\\
5x&=3
\\\\
\dfrac{\cancel5x}{\cancel5}&=\dfrac{3}{5}
\\\\
x&=\dfrac{3}{5}
.\end{align*}
Hence, the solution to the equation $8(x-1)-3(x-2)=1$ is $x=\dfrac{3}{5}$.
