Answer
all real numbers
Work Step by Step
Using the properties of inequality and solving separately, the given expression, $
2x+1>5 \text{ or }x-7\le3
,$ is equivalent to
\begin{align*}\require{cancel}
\begin{array}{l|r}
2x+1>5 & x-7\le3
\\
2x+1-1>5-1 & x-7+7\le3+7
\\
2x>4 & x\le10
\\\\
\dfrac{\cancel2x}{\cancel2}>\dfrac{4}{2} &
\\\\
x>2. &
\end{array}
\end{align*}
Since the compound word "or" is used, combine the two solutions above. Hence, the solution is the set of all real numbers.
