Solve for p 10+6p<-7p-3<=p-19

$10 + 6 p < - 7 p - 3 \leq p - 19$

Solve $10 + 6 p < - 7 p - 3$ for $p$ .

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

Add $7 p$ to both sides of the inequality.

$10 + 6 p + 7 p < - 3$

Add $6 p$ and $7 p$ .

$10 + 13 p < - 3$

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

Subtract $10$ from both sides of the inequality.

$13 p < - 3 - 10$

Subtract $10$ from $- 3$ .

$13 p < - 13$

Divide each term in $13 p < - 13$ by $13$ and simplify.

Divide each term in $13 p < - 13$ by $13$ .

$\frac{13 p}{13} < \frac{- 13}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 p}{13} < \frac{- 13}{13}$

Divide $p$ by $1$ .

$p < \frac{- 13}{13}$

Simplify the right side.

Divide $- 13$ by $13$ .

$p < - 1$

Solve $- 7 p - 3 \leq p - 19$ for $p$ .

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

Subtract $p$ from both sides of the inequality.

$- 7 p - 3 - p \leq - 19$

Subtract $p$ from $- 7 p$ .

$- 8 p - 3 \leq - 19$

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

Add $3$ to both sides of the inequality.

$- 8 p \leq - 19 + 3$

Add $- 19$ and $3$ .

$- 8 p \leq - 16$

Divide each term in $- 8 p \leq - 16$ by $- 8$ and simplify.

Divide each term in $- 8 p \leq - 16$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 p}{- 8} \geq \frac{- 16}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 p}{- 8} \geq \frac{- 16}{- 8}$

Divide $p$ by $1$ .

$p \geq \frac{- 16}{- 8}$

Simplify the right side.

Divide $- 16$ by $- 8$ .

$p \geq 2$

Find the intersection of $p < - 1$ and $p \geq 2$ .

No solution

Solve for p 10+6p<-7p-3<=p-19

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