Answer
$[1,\infty)$
Work Step by Step
Using the properties of inequality, the given inequality, $
-2x+4\le-x+3
$ is equivalent to
\begin{align*}
-2x+x&\le3-4
\\
-x&\le-1
.\end{align*}
Multiplying both sides by $-1$ (and consequentially reversing the inequality), then
\begin{align*}
-1(-x)&\ge(-1)(-1)
\\
x&\ge1
.\end{align*}
Hence, in interval notation, the solution of $
-2x+4\le-x+3
$ is $[1,\infty)$.
