Answer
The solution is $\Big(-\infty,\dfrac{1}{2}\Big]$
Work Step by Step
$\dfrac{2x-5}{-8}\le1-x$
Change the sign of the denominator and the sign of the fraction on the left side:
$-\dfrac{2x-5}{8}\le1-x$
Rearrange:
$x-1\le\dfrac{2x-5}{8}$
Take $8$ to multiply the left side:
$8(x-1)\le2x-5$
$8x-8\le2x-5$
Take $2x$ to the left side and $8$ to the right side:
$8x-2x\le-5+8$
$6x\le3$
Take $6$ to divide the right side and simplify:
$x\le\dfrac{3}{6}$
$x\le\dfrac{1}{2}$
Expressing the solution in interval notation:
$\Big(-\infty,\dfrac{1}{2}\Big]$
