Question

solve for w and graph the solution.
20w - 1 - 17w ≤ -10 or w + 9 - 4w ≤ 15
plot the endpoints. select an endpoint to change it from closed to open. se
a segment, ray, or line to delete it.

Explanation:

Step1: Simplify the first inequality

Combine like terms: \(20w - 17w-1\leq - 10\), which is \(3w-1\leq - 10\).
Add 1 to both sides: \(3w\leq - 10 + 1\), so \(3w\leq - 9\).
Divide both sides by 3: \(w\leq - 3\).

Step2: Simplify the second inequality

Combine like terms: \(w-4w + 9\leq 15\), which is \(-3w+9\leq 15\).
Subtract 9 from both sides: \(-3w\leq 15 - 9\), so \(-3w\leq 6\).
Divide both sides by \(-3\) (and reverse the inequality sign): \(w\geq - 2\).

Answer:

The solution is \(w\leq - 3\) or \(w\geq - 2\). On the number - line, for \(w\leq - 3\), we have a closed circle at \(w = - 3\) and a ray to the left. For \(w\geq - 2\), we have a closed circle at \(w=-2\) and a ray to the right.