Answer
$x>\displaystyle \frac{1}{3}$
Work Step by Step
Applying the properties of inequality, we can
P1. add any number to both sides,
P2. multiply (or divide) both sides with a positive
$\quad $ number to arrive at a valid inequality.
$\quad $ If we
P3. multiply (or divide) both sides with a negative number,
we must change the direction of the inequality sign, to arrive at a valid inequality..
Our goal is to, step by step, isolate the unknown on one side and interpret the result
(which, if any, will be an interval)
-----------------------------
$x+5(x+1)>4(2-x)+x\qquad \qquad $... parentheses
$x+5x+5>8-4x+x \qquad $... simplify
$6x+5>8-3x \qquad \qquad $P1: ...$/-5$
$6x>3-3x \qquad \qquad $P1: ...$/+3x$
$9x>3 \qquad \qquad $P$2$: ...$/\div 9$
$x>\displaystyle \frac{1}{3}$
In interval notation:$\qquad (\displaystyle \frac{1}{3}$ , $\infty)$.
