Question

solve for w and graph the solution. -6|w + 35| ≥ -90 click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Isolate the absolute value

Start with the inequality \(-6|w + 35| \geq -90\). Divide both sides by \(-6\). Remember that when dividing or multiplying an inequality by a negative number, the inequality sign flips. So we get \(|w + 35| \leq 15\).

Step2: Solve the compound inequality

The absolute value inequality \(|w + 35| \leq 15\) is equivalent to the compound inequality \(-15 \leq w + 35 \leq 15\). Now, subtract 35 from all parts of the compound inequality. For the left part: \(-15 - 35 \leq w\), which simplifies to \(-50 \leq w\). For the right part: \(w \leq 15 - 35\), which simplifies to \(w \leq -20\). So the solution is \(-50 \leq w \leq -20\).

Step3: Graph the solution

To graph this on the number line, we use filled - in circles at \(-50\) and \(-20\) (because the inequality is "less than or equal to", so the endpoints are included) and draw a line segment connecting them.

Answer:

The solution for \(w\) is \(-50\leq w\leq - 20\). To graph it, mark filled - in circles at \(-50\) and \(-20\) on the number line and draw a line segment between them.