Question

solve the inequality and graph the solution on the line provided.
-5 - 8x ≥ 43
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:

Explanation:

Step1: Isolate the term with \(x\)

Add \(5\) to both sides of the inequality \(-5 - 8x\geq43\).
Using the addition property of inequalities: \(-5+5 - 8x\geq43 + 5\), which simplifies to \(-8x\geq48\).

Step2: Solve for \(x\)

Divide both sides of the inequality \(-8x\geq48\) by \(-8\). Remember that when dividing an inequality by a negative number, the direction of the inequality sign changes.
So, \(\frac{-8x}{-8}\leq\frac{48}{-8}\), which gives \(x\leq - 6\).

Answer:

Inequality Notation: \(x\leq - 6\)

For the number - line: Place a closed circle (because the inequality is \(\leq\)) at \(-6\) and shade to the left (since \(x\) is less than or equal to \(-6\)).