Question

which graph represents the compound inequality below?
$4x - 5 \leq -25$ or $-9x + 1 \leq -35$
show your work here
hint: to add infinity ($\infty$), type \infinity\

Explanation:

Step1: Solve the first inequality

For \(4x - 5\leq - 25\), add \(5\) to both sides:
\(4x-5 + 5\leq - 25+5\), so \(4x\leq - 20\).
Divide both sides by \(4\): \(x\leq - 5\).

Step2: Solve the second inequality

For \(-9x + 1\leq - 35\), subtract \(1\) from both sides:
\(-9x+1 - 1\leq - 35 - 1\), so \(-9x\leq - 36\).
Divide both sides by \(-9\) (and reverse the inequality sign): \(x\geq4\).

Answer:

The solution of the compound inequality \(4x - 5\leq - 25\) or \(-9x + 1\leq - 35\) is \(x\leq - 5\) or \(x\geq4\). So the graph should have a closed - circle at \(x = - 5\) and shade to the left (for \(x\leq - 5\)) and a closed - circle at \(x = 4\) and shade to the right (for \(x\geq4\)).