Question

which graph represents the compound inequality below?
$9x - 7 > 38$ or $-2x + 7 \geq 19$
show your work here
hint: to add the empty set symbol ($\varnothing$), type \emptyset\

Explanation:

Step1: Solve \(9x - 7>38\)

Add \(7\) to both sides: \(9x>38 + 7\), so \(9x>45\).
Divide both sides by \(9\): \(x > 5\).

Step2: Solve \(-2x+7\geq19\)

Subtract \(7\) from both sides: \(-2x\geq19 - 7\), so \(-2x\geq12\).
Divide both sides by \(- 2\) (and reverse the inequality sign): \(x\leq - 6\).

Answer:

The first option (the number line with a closed circle at \(-6\) (since \(x\leq - 6\)) and an open circle at \(5\) (since \(x>5\)) and arrows going in opposite directions) is the correct graph.