Question

anne arundel county public schools | division of academics
#8
solve and graph.
-2x + 8 ≥ 0

Explanation:

Step1: Isolate the term with \(x\)

Subtract \(8\) from both sides of the inequality:
\(-2x+8 - 8\geq0 - 8\)
\(-2x\geq - 8\)

Step2: Solve for \(x\)

Divide both sides by \(-2\). Remember that when dividing by a negative number, the inequality sign flips.
\(x\leq\frac{-8}{-2}\)
\(x\leq4\)

Answer:

The solution is \(x\leq4\). To graph it, draw a number line. Put a closed circle at \(x = 4\) (because the inequality includes equality, \(\geq\) flips to \(\leq\) after division by negative and the original inequality allows \(x = 4\) as \(-2\times4+8=-8 + 8=0\)) and shade to the left of \(4\) (since \(x\) is less than or equal to \(4\)).