Algebra Examples

$7 p + 5 \leq - 37$ and $- 10 p < 10$

Step 1

Simplify the first inequality.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Subtract $5$ from both sides of the inequality.

$7 p \leq - 37 - 5$ and $- 10 p < 10$

Step 1.1.2

Subtract $5$ from $- 37$ .

$7 p \leq - 42$ and $- 10 p < 10$

Step 1.2

Divide each term in $7 p \leq - 42$ by $7$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $7 p \leq - 42$ by $7$ .

$\frac{7 p}{7} \leq \frac{- 42}{7}$ and $- 10 p < 10$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{7 p}{7} \leq \frac{- 42}{7}$ and $- 10 p < 10$

Step 1.2.2.1.2

Divide $p$ by $1$ .

$p \leq \frac{- 42}{7}$ and $- 10 p < 10$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Divide $- 42$ by $7$ .

$p \leq - 6$ and $- 10 p < 10$

Step 2

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

Tap for more steps...

Step 2.1

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

$p \leq - 6$ and $\frac{- 10 p}{- 10} > \frac{10}{- 10}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $- 10$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$p \leq - 6$ and $\frac{- 10 p}{- 10} > \frac{10}{- 10}$

Step 2.2.1.2

Divide $p$ by $1$ .

$p \leq - 6$ and $p > \frac{10}{- 10}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $10$ by $- 10$ .

$p \leq - 6$ and $p > - 1$

Step 3

The intersection consists of the elements that are contained in both intervals.

No solution