Question

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solve for p and graph the solution. -10 > 7p - 3 ≥ -17. plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Solve the inequality

Starting with \(-10>7p - 3\geq - 17\). First, solve the left - hand side of the compound inequality \(-10>7p - 3\). Add 3 to both sides: \(-10 + 3>7p-3 + 3\), which simplifies to \(-7>7p\). Divide both sides by 7: \(\frac{-7}{7}>p\), so \(p < - 1\).

Step2: Solve the right - hand side of the inequality

Now solve \(7p - 3\geq - 17\). Add 3 to both sides: \(7p-3 + 3\geq - 17+3\), which gives \(7p\geq - 14\). Divide both sides by 7: \(p\geq - 2\).

Step3: Combine the solutions

The solution of the compound inequality is \(-2\leq p < - 1\).

Step4: Plot on the number line

On the number line, we have a closed circle at \(p=-2\) (because \(p\) can equal \(-2\)) and an open circle at \(p = - 1\) (because \(p\) cannot equal \(-1\)), and we draw a line segment between them.

Answer:

The solution is \(-2\leq p < - 1\). On the number line, there is a closed circle at \(-2\) and an open circle at \(-1\) with a line segment between them.