Answer
$[0,2)$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$x-1\leq 7x-1$ and $4x-7\lt 3-x$.
Solve each inequality separately.
$\Rightarrow x-1\leq 7x-1$ and $4x-7\lt 3-x$.
$\Rightarrow x-1+1\leq 7x$ and $4x\lt 3-x+7$.
$\Rightarrow x+0\leq 7x$ and $4x\lt 10-x$.
$\Rightarrow 0\leq 7x-x$ and $4x+x\lt 10$.
$\Rightarrow 0\leq 6x$ and $5x\lt 10$.
$\Rightarrow 0\leq x$ and $x\lt 2$.
First graph then take the intersection of the solution sets of the two inequalities..
The graph is shown in the image file.
We can write the compound inequality.
$0\leq x$ as $[0,\infty)$ and $x\lt 2$ as $(-\infty,2)$
The intersection is
$(-\infty,2)\cap[0,\infty)=[0,2)$.
