Answer
True
Work Step by Step
Solve each equation/inequality to obtain:
\begin{align*}
x+1&=6\\
x&=6-1\\
x&=5
\end{align*}
Thus, the solution set is $\left\{5\right\}$.
\begin{align*}
x+1&\lt6\\
x&\lt6-1\\
x&\lt5
\end{align*}
Thus, the solution set is $\left\{x|x\lt5\right\}$.
\begin{align*}
x+1&\gt6\\
x&\gt6-1\\
x&\gt5
\end{align*}
Thus, the solution set is $\left\{x|x\gt5\right\}$.
Therefore, the union of the solution sets of is:
\begin{align*}
&=\left\{5\right\} \cup (-\infty, 5) \cup (5, +\infty)\\
&=(-\infty, +\infty)
\end{align*}
Hence, the given statement is true.
