Answer
$x\gt \dfrac{y-b}{a}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
y\lt ax+b
$ for $
x
,$ where $a\gt0.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
y\lt ax+b
\\\\
-ax\lt b-y
.\end{array}
Since $a\gt0,$ then the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-ax\lt b-y
.\end{array}
Dividing both sides by $-a$ (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-ax\lt b-y
\\\\
x\gt \dfrac{b-y}{-a}
\\\\
x\gt \dfrac{y-b}{a}
.\end{array}
