Question

solve the following inequality for x. $x - 7 leq 5(7 - x)$
a. $x < - 5$
b. $x leq 7$
c. $x < 8$
d. $x geq 9$

Explanation:

Step1: Expand the right - hand side

$x - 7\leq35 - 5x$

Step2: Add $5x$ to both sides

$x+5x - 7\leq35-5x + 5x$
$6x - 7\leq35$

Step3: Add 7 to both sides

$6x-7 + 7\leq35 + 7$
$6x\leq42$

Step4: Divide both sides by 6

$\frac{6x}{6}\leq\frac{42}{6}$
$x\leq7$

Answer:

B. $x\leq7$