Solve for p -17+11p<p-14<=11p-11

$- 17 + 11 p < p - 14 \leq 11 p - 11$

Step 1

Solve $- 17 + 11 p < p - 14$ for $p$ .

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

Subtract $p$ from both sides of the inequality.

$- 17 + 11 p - p < - 14$

Subtract $p$ from $11 p$ .

$- 17 + 10 p < - 14$

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

Add $17$ to both sides of the inequality.

$10 p < - 14 + 17$

Add $- 14$ and $17$ .

$10 p < 3$

Divide each term in $10 p < 3$ by $10$ and simplify.

Divide each term in $10 p < 3$ by $10$ .

$\frac{10 p}{10} < \frac{3}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 p}{10} < \frac{3}{10}$

Divide $p$ by $1$ .

$p < \frac{3}{10}$

Step 2

Solve $p - 14 \leq 11 p - 11$ for $p$ .

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

Subtract $11 p$ from both sides of the inequality.

$p - 14 - 11 p \leq - 11$

Subtract $11 p$ from $p$ .

$- 10 p - 14 \leq - 11$

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

Add $14$ to both sides of the inequality.

$- 10 p \leq - 11 + 14$

Add $- 11$ and $14$ .

$- 10 p \leq 3$

Divide each term in $- 10 p \leq 3$ by $- 10$ and simplify.

Divide each term in $- 10 p \leq 3$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 p}{- 10} \geq \frac{3}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 p}{- 10} \geq \frac{3}{- 10}$

Divide $p$ by $1$ .

$p \geq \frac{3}{- 10}$

Simplify the right side.

Move the negative in front of the fraction.

$p \geq - \frac{3}{10}$

Step 3

Find the intersection of $p < \frac{3}{10}$ and $p \geq - \frac{3}{10}$ .

$- \frac{3}{10} \leq p < \frac{3}{10}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{10} \leq p < \frac{3}{10}$

Interval Notation:

$[- \frac{3}{10}, \frac{3}{10})$

Step 5

Solve for p -17+11p<p-14<=11p-11

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