Answer
$x\lt\dfrac{13}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distributive Property to simplify the given inequality, $
9(x-3)-4x\lt2-(3-x)
.$ Then use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to
\begin{array}{l}\require{cancel}
9(x-3)-4x\lt2-(3-x)
\\\\
9(x)+9(-3)-4x\lt2-1(3)-1(-x)
\\\\
9x-27-4x\lt2-3+x
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
9x-27-4x\lt2-3+x
\\\\
9x-4x-x\lt2-3+27
\\\\
4x\lt26
\\\\
x\lt\dfrac{26}{4}
\\\\
x\lt\dfrac{13}{2}
.\end{array}
