Solve for p 4p+2<2(p+5)

$4 p + 2 < 2 (p + 5)$

Step 1

Simplify $2 (p + 5)$ .

Rewrite.

$4 p + 2 < 0 + 0 + 2 (p + 5)$

Simplify by adding zeros.

$4 p + 2 < 2 (p + 5)$

Apply the distributive property.

$4 p + 2 < 2 p + 2 \cdot 5$

Multiply $2$ by $5$ .

$4 p + 2 < 2 p + 10$

Step 2

Move all terms containing $p$ to the left side of the inequality.

Subtract $2 p$ from both sides of the inequality.

$4 p + 2 - 2 p < 10$

Subtract $2 p$ from $4 p$ .

$2 p + 2 < 10$

Step 3

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

Subtract $2$ from both sides of the inequality.

$2 p < 10 - 2$

Subtract $2$ from $10$ .

$2 p < 8$

Step 4

Divide each term in $2 p < 8$ by $2$ and simplify.

Divide each term in $2 p < 8$ by $2$ .

$\frac{2 p}{2} < \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 p}{2} < \frac{8}{2}$

Divide $p$ by $1$ .

$p < \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$p < 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$p < 4$

Interval Notation:

$(- \infty, 4)$