Question

1. $-11(8p + 7) \geq -5p + 7(4p - 11)$

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the inequality.
For the left - hand side: \(-11(8p + 7)=-11\times8p-11\times7=-88p - 77\)
For the right - hand side: \(-5p+7(4p - 11)=-5p+7\times4p-7\times11=-5p + 28p-77 = 23p-77\)
So the inequality becomes \(-88p-77\geq23p - 77\)

Step2: Move all terms with p to one side

Subtract \(23p\) from both sides of the inequality: \(-88p-23p-77\geq23p-23p - 77\)
\(-111p-77\geq - 77\)

Step3: Move the constant term to the other side

Add 77 to both sides of the inequality: \(-111p-77 + 77\geq-77 + 77\)
\(-111p\geq0\)

Step4: Solve for p

Divide both sides of the inequality by - 111. Remember that when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
\(p\leq\frac{0}{-111}\)
\(p\leq0\)

Answer:

\(p\leq0\)