Precalculus Examples

$2 x + 3 y > 12$ , $3 x - y < 22$

Step 1

Solve $2 x + 3 y > 12$ for $y$ .

Tap for more steps...

Step 1.1

Subtract $2 x$ from both sides of the inequality.

$3 y > 12 - 2 x$

Step 1.2

Divide each term in $3 y > 12 - 2 x$ by $3$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $3 y > 12 - 2 x$ by $3$ .

$\frac{3 y}{3} > \frac{12}{3} + \frac{- 2 x}{3}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} > \frac{12}{3} + \frac{- 2 x}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{12}{3} + \frac{- 2 x}{3}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Divide $12$ by $3$ .

$y > 4 + \frac{- 2 x}{3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y > 4 - \frac{2 x}{3}$

Step 2

Solve $3 x - y < 22$ for $y$ .

Tap for more steps...

Step 2.1

Subtract $3 x$ from both sides of the inequality.

$- y < 22 - 3 x$

Step 2.2

Divide each term in $- y < 22 - 3 x$ by $- 1$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- y < 22 - 3 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{22}{- 1} + \frac{- 3 x}{- 1}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{22}{- 1} + \frac{- 3 x}{- 1}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y > \frac{22}{- 1} + \frac{- 3 x}{- 1}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Simplify each term.

Tap for more steps...

Step 2.2.3.1.1

Divide $22$ by $- 1$ .

$y > - 22 + \frac{- 3 x}{- 1}$

Step 2.2.3.1.2

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y > - 22 - 1 \cdot (- 3 x)$

Step 2.2.3.1.3

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y > - 22 - (- 3 x)$

Step 2.2.3.1.4

Multiply $- 3$ by $- 1$ .

$y > - 22 + 3 x$

Step 3

Find the intersection of $y > 4 - \frac{2 x}{3}$ and $y > - 22 + 3 x$ .

$y > 4 - \frac{2 x}{3}$ and $y > - 22 + 3 x$

Step 4