Answer
The solution of the equation $3\left( 2x-3 \right)=9-5\left( 2-x \right)$ is $8$.
Work Step by Step
Consider the equation.
$3\left( 2x-3 \right)=9-5\left( 2-x \right)$
Apply the distributive property.
$6x-9=9-10+5x$
Combine the like terms and simplify the terms.
$6x-9=-1+5x$
Apply the addition principle:
$6x-9-5x=-1+5x-5x$
Simplify the terms.
$\begin{align}
& 6x-5x-9=-1+5x-5x \\
& x-9=-1 \\
\end{align}$
$\begin{align}
& x-9+9=-1+9 \\
& x=8
\end{align}$
Check:
Substitute $8$ for $x$ in the given equation.
$\begin{matrix}
3\left( 2\left( 8 \right)-3 \right)\overset{?}{\mathop{=}}\,-5\left( 2-8 \right) \\
3\left( 16-3 \right)\overset{?}{\mathop{=}}\,9-5\left( -6 \right) \\
3\left( 13 \right)\overset{?}{\mathop{=}}\,9+30 \\
39=39 \\
\end{matrix}$
It is true.
