Answer
$\left(-\infty,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
x\lt x+1
.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
x\lt x+1
\\\\
x-x\lt 1
\\\\
0\lt 1
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, any number substituted to $x$ will satisfy the given inequality. Hence, the solution set is $
\left(-\infty,\infty \right)
.$
