Answer
$x\gt\dfrac{16}{5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the properties of inequality to solve the given, $
3(7-x)\lt2x+5
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3(7-x)\lt2x+5
\\\\
3(7)+3(-x)\lt2x+5
\\\\
21-3x\lt2x+5
.\end{array}
Using the properties of equality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
21-3x\lt2x+5
\\\\
-3x-2x\lt5-21
\\\\
-5x\lt-16
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-5x\lt-16
\\\\
x\gt\dfrac{-16}{-5}
\\\\
x\gt\dfrac{16}{5}
.\end{array}
