Question

what is the solution set for the inequality $42 + 6x \geq 3(-x - 4)$?\
\\(\bigcirc\\) $x \leq -18$\
\\(\bigcirc\\) $x \leq -6$\
\\(\bigcirc\\) $x \geq -6$\
\\(\bigcirc\\) $x \geq -18$

Explanation:

Step1: Expand right-hand side

$42 + 6x \geq -3x - 12$

Step2: Add $3x$ to both sides

$42 + 6x + 3x \geq -12$
$42 + 9x \geq -12$

Step3: Subtract 42 from both sides

$9x \geq -12 - 42$
$9x \geq -54$

Step4: Divide by 9 on both sides

$x \geq \frac{-54}{9}$
$x \geq -6$

Answer:

$x \geq -6$ (corresponding to the option: $x \geq -6$)