Question

which graph represents the compound inequality below?
$10x + 10 < 80$ or $-8x + 10 \leq -54$

Explanation:

Step1: Solve the first inequality

Subtract \(10\) from both sides of \(10x + 10\lt80\):
\(10x+10 - 10\lt80 - 10\), so \(10x\lt70\).
Divide both sides by \(10\): \(x\lt7\).

Step2: Solve the second inequality

Subtract \(10\) from both sides of \(-8x + 10\leqslant-54\):
\(-8x+10 - 10\leqslant-54 - 10\), so \(-8x\leqslant-64\).
Divide both sides by \(-8\) (and reverse the inequality sign): \(x\geqslant8\).

Answer:

The solution of the compound inequality \(10x + 10\lt80\) or \(-8x + 10\leqslant-54\) is \(x\lt7\) or \(x\geqslant8\). On the number - line, there is an open circle at \(x = 7\) (because \(x\lt7\)) and a closed circle at \(x = 8\) (because \(x\geqslant8\)), with the line extending to the left of \(7\) and to the right of \(8\).