Solve the Inequality for p 2(p+1)+3(p+2)>2

$2 (p + 1) + 3 (p + 2) > 2$

Step 1

Simplify $2 (p + 1) + 3 (p + 2)$ .

Simplify each term.

Apply the distributive property.

$2 p + 2 \cdot 1 + 3 (p + 2) > 2$

Multiply $2$ by $1$ .

$2 p + 2 + 3 (p + 2) > 2$

Apply the distributive property.

$2 p + 2 + 3 p + 3 \cdot 2 > 2$

Multiply $3$ by $2$ .

$2 p + 2 + 3 p + 6 > 2$

Simplify by adding terms.

Add $2 p$ and $3 p$ .

$5 p + 2 + 6 > 2$

Add $2$ and $6$ .

$5 p + 8 > 2$

Step 2

Move all terms not containing $p$ to the right side of the inequality.

Subtract $8$ from both sides of the inequality.

$5 p > 2 - 8$

Subtract $8$ from $2$ .

$5 p > - 6$

Step 3

Divide each term in $5 p > - 6$ by $5$ and simplify.

Divide each term in $5 p > - 6$ by $5$ .

$\frac{5 p}{5} > \frac{- 6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 p}{5} > \frac{- 6}{5}$

Divide $p$ by $1$ .

$p > \frac{- 6}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$p > - \frac{6}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$p > - \frac{6}{5}$

Interval Notation:

$(- \frac{6}{5}, \infty)$