Finite Math Examples

$y > 6 x - 2$ , $y < - 3 x + 4$

Step 1

Simplify the first inequality.

Tap for more steps...

Step 1.1

Rewrite so $x$ is on the left side of the inequality.

$6 x - 2 < y$ and $y < - 3 x + 4$

Step 1.2

Add $2$ to both sides of the inequality.

$6 x < y + 2$ and $y < - 3 x + 4$

Step 1.3

Divide each term in $6 x < y + 2$ by $6$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $6 x < y + 2$ by $6$ .

$\frac{6 x}{6} < \frac{y}{6} + \frac{2}{6}$ and $y < - 3 x + 4$

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 1.3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} < \frac{y}{6} + \frac{2}{6}$ and $y < - 3 x + 4$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{y}{6} + \frac{2}{6}$ and $y < - 3 x + 4$

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Cancel the common factor of $2$ and $6$ .

Tap for more steps...

Step 1.3.3.1.1

Factor $2$ out of $2$ .

$x < \frac{y}{6} + \frac{2 (1)}{6}$ and $y < - 3 x + 4$

Step 1.3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.3.3.1.2.1

Factor $2$ out of $6$ .

$x < \frac{y}{6} + \frac{2 \cdot 1}{2 \cdot 3}$ and $y < - 3 x + 4$

Step 1.3.3.1.2.2

Cancel the common factor.

$x < \frac{y}{6} + \frac{2 \cdot 1}{2 \cdot 3}$ and $y < - 3 x + 4$

Step 1.3.3.1.2.3

Rewrite the expression.

$x < \frac{y}{6} + \frac{1}{3}$ and $y < - 3 x + 4$

Step 2

Simplify the second inequality.

Tap for more steps...

Step 2.1

Rewrite so $x$ is on the left side of the inequality.

$x < \frac{y}{6} + \frac{1}{3}$ and $- 3 x + 4 > y$

Step 2.2

Subtract $4$ from both sides of the inequality.

$x < \frac{y}{6} + \frac{1}{3}$ and $- 3 x > y - 4$

Step 2.3

Divide each term in $- 3 x > y - 4$ by $- 3$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $- 3 x > y - 4$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < \frac{y}{6} + \frac{1}{3}$ and $\frac{- 3 x}{- 3} < \frac{y}{- 3} + \frac{- 4}{- 3}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$x < \frac{y}{6} + \frac{1}{3}$ and $\frac{- 3 x}{- 3} < \frac{y}{- 3} + \frac{- 4}{- 3}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{y}{6} + \frac{1}{3}$ and $x < \frac{y}{- 3} + \frac{- 4}{- 3}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Simplify each term.

Tap for more steps...

Step 2.3.3.1.1

Move the negative in front of the fraction.

$x < \frac{y}{6} + \frac{1}{3}$ and $x < - \frac{y}{3} + \frac{- 4}{- 3}$

Step 2.3.3.1.2

Dividing two negative values results in a positive value.

$x < \frac{y}{6} + \frac{1}{3}$ and $x < - \frac{y}{3} + \frac{4}{3}$

Step 3