Question

solve the inequality, write the solution in interval notation, then graph. -2p - (p + 2) > -2 - p

Explanation:

Step1: Simplify left - hand side

First, distribute the negative sign in $-2p-(p + 2)$:
$-2p - p-2=-3p - 2$.
The inequality becomes $-3p - 2>-2 - p$.

Step2: Add $p$ to both sides

Adding $p$ to both sides gives:
$-3p - 2+p>-2 - p+p$.
Combining like - terms, we have $-2p - 2>-2$.

Step3: Add 2 to both sides

Adding 2 to both sides:
$-2p-2 + 2>-2 + 2$.
This simplifies to $-2p>0$.

Step4: Divide both sides by -2

Dividing both sides by $-2$ and reversing the inequality sign (since dividing by a negative number), we get:
$p<0$.

Answer:

The solution in interval notation is $(-\infty,0)$. To graph, draw an open circle at $0$ on the number line and shade to the left.