Question

solve the following inequality for x.
3(-8x + 7) - 43 ≤ -25x

a. x ≤ -22/51
b. x ≤ 22
c. x ≤ -22
d. x ≤ 22/51

Explanation:

Step1: Expand the left - hand side

$3(-8x + 7)-43=3\times(-8x)+3\times7 - 43=-24x+21 - 43=-24x - 22$
The inequality becomes $-24x - 22\leq - 25x$.

Step2: Add $25x$ to both sides

$-24x+25x - 22\leq - 25x+25x$
$x - 22\leq0$

Step3: Add 22 to both sides

$x - 22+22\leq0 + 22$
$x\leq22$

Answer:

B. $x\leq22$