Question

which graph represents the compound inequality below?
$6x + 9 \geq 33$ or $3x - 8 \leq -29$
show your work here
hint: to add the union symbol (∪), type \union\

Explanation:

Step1: Solve the first inequality

Solve \(6x + 9\geq33\).
Subtract 9 from both sides: \(6x\geq33 - 9\), so \(6x\geq24\).
Divide both sides by 6: \(x\geq4\).

Step2: Solve the second inequality

Solve \(3x - 8\leq - 29\).
Add 8 to both sides: \(3x\leq-29 + 8\), so \(3x\leq-21\).
Divide both sides by 3: \(x\leq-7\).

The solution of the compound inequality \(6x + 9\geq33\) or \(3x - 8\leq - 29\) is \(x\leq-7\) union \(x\geq4\).

Answer:

The first graph (the one with a closed - circle at \(x = - 7\) and an arrow to the left, and a closed - circle at \(x = 4\) and an arrow to the right) represents the compound inequality.