Solve the Inequality for p -9+5(5p+1)<-9p+8+9

$- 9 + 5 (5 p + 1) < - 9 p + 8 + 9$

Simplify $- 9 + 5 (5 p + 1)$ .

Simplify each term.

Apply the distributive property.

$- 9 + 5 (5 p) + 5 \cdot 1 < - 9 p + 8 + 9$

Multiply $5$ by $5$ .

$- 9 + 25 p + 5 \cdot 1 < - 9 p + 8 + 9$

Multiply $5$ by $1$ .

$- 9 + 25 p + 5 < - 9 p + 8 + 9$

Add $- 9$ and $5$ .

$25 p - 4 < - 9 p + 8 + 9$

Add $8$ and $9$ .

$25 p - 4 < - 9 p + 17$

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

Add $9 p$ to both sides of the inequality.

$25 p - 4 + 9 p < 17$

Add $25 p$ and $9 p$ .

$34 p - 4 < 17$

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

Add $4$ to both sides of the inequality.

$34 p < 17 + 4$

Add $17$ and $4$ .

$34 p < 21$

Divide each term in $34 p < 21$ by $34$ and simplify.

Divide each term in $34 p < 21$ by $34$ .

$\frac{34 p}{34} < \frac{21}{34}$

Simplify the left side.

Cancel the common factor of $34$ .

Cancel the common factor.

$\frac{34 p}{34} < \frac{21}{34}$

Divide $p$ by $1$ .

$p < \frac{21}{34}$

The result can be shown in multiple forms.

Inequality Form:

$p < \frac{21}{34}$

Interval Notation:

$(- \infty, \frac{21}{34})$