Finite Math Examples

$4 x - y < 6$ , $3 x + y < 9$

Step 1

Solve $4 x - y < 6$ for $y$ .

Tap for more steps...

Step 1.1

Subtract $4 x$ from both sides of the inequality.

$- y < 6 - 4 x$

Step 1.2

Divide each term in $- y < 6 - 4 x$ by $- 1$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- y < 6 - 4 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.2.2

Divide $y$ by $1$ .

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

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 $6$ by $- 1$ .

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

Step 1.2.3.1.2

Move the negative one from the denominator of $\frac{- 4 x}{- 1}$ .

$y > - 6 - 1 \cdot (- 4 x)$

Step 1.2.3.1.3

Rewrite $- 1 \cdot (- 4 x)$ as $- (- 4 x)$ .

$y > - 6 - (- 4 x)$

Step 1.2.3.1.4

Multiply $- 4$ by $- 1$ .

$y > - 6 + 4 x$

Step 2

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

$y < 9 - 3 x$

Step 3

Find the intersection of $y > - 6 + 4 x$ and $y < 9 - 3 x$ .

$- 6 + 4 x < y < 9 - 3 x$

Step 4