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:

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