Solve the Inequality for P 6(2P-1)>5P+2

$6 (2 P - 1) > 5 P + 2$

Step 1

Simplify $6 (2 P - 1)$ .

Rewrite.

$0 + 0 + 6 (2 P - 1) > 5 P + 2$

Simplify by adding zeros.

$6 (2 P - 1) > 5 P + 2$

Apply the distributive property.

$6 (2 P) + 6 \cdot - 1 > 5 P + 2$

Multiply.

Multiply $2$ by $6$ .

$12 P + 6 \cdot - 1 > 5 P + 2$

Multiply $6$ by $- 1$ .

$12 P - 6 > 5 P + 2$

Step 2

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

Subtract $5 P$ from both sides of the inequality.

$12 P - 6 - 5 P > 2$

Subtract $5 P$ from $12 P$ .

$7 P - 6 > 2$

Step 3

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

Add $6$ to both sides of the inequality.

$7 P > 2 + 6$

Add $2$ and $6$ .

$7 P > 8$

Step 4

Divide each term in $7 P > 8$ by $7$ and simplify.

Divide each term in $7 P > 8$ by $7$ .

$\frac{7 P}{7} > \frac{8}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 P}{7} > \frac{8}{7}$

Divide $P$ by $1$ .

$P > \frac{8}{7}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$P > \frac{8}{7}$

Interval Notation:

$(\frac{8}{7}, \infty)$