## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\left(-\infty,\infty \right)$
$\bf{\text{Solution Outline:}}$ 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 $\left(-\infty,\infty \right) .$