Question

this question has two parts. first, answer part a. then, answer part b.
part a
translate the sentence into an inequality.
eight minus a number x divided by three is greater than or equal to eleven.
part b
solve the inequality and graph the solution on a number line.
a) ( x leq -9 )
number line with arrow left from -9 (open circle? wait, no, the image shows for a: arrow left, -9 with open circle? wait, no, the users image: for a, the number line has -15, -13, -11, -9 (open circle?), arrow left. for b: -9 closed circle, arrow right. for c: -9 closed circle, arrow left.
b) ( x geq -9 )
c) ( x leq -9 )

Explanation:

Step1: Translate to inequality

$8 - \frac{x}{3} \geq 11$

Step2: Subtract 8 from both sides

$8 - \frac{x}{3} - 8 \geq 11 - 8$
$-\frac{x}{3} \geq 3$

Step3: Multiply by -3 (reverse inequality)

$-\frac{x}{3} \times (-3) \leq 3 \times (-3)$
$x \leq -9$

Step4: Match graph for solution

A closed dot at -9, arrow left (for $x \leq -9$)

Answer:

Part A:

$8 - \frac{x}{3} \geq 11$

Part B:

C) $x \leq -9$ (with the number line showing a closed dot at -9 and an arrow pointing left towards negative infinity)