Algebra Examples

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

Step 1

Solve $y > 4 x + 3 y$ for $y$ .

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Step 1.1

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

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Step 1.1.1

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

$y - 3 y > 4 x$

Step 1.1.2

Subtract $3 y$ from $y$ .

$- 2 y > 4 x$

Step 1.2

Divide each term in $- 2 y > 4 x$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 y > 4 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} < \frac{4 x}{- 2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} < \frac{4 x}{- 2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{4 x}{- 2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Cancel the common factor of $4$ and $- 2$ .

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Step 1.2.3.1.1

Factor $2$ out of $4 x$ .

$y < \frac{2 (2 x)}{- 2}$

Step 1.2.3.1.2

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

$y < - 1 \cdot (2 x)$

Step 1.2.3.2

Simplify the expression.

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Step 1.2.3.2.1

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y < - (2 x)$

Step 1.2.3.2.2

Multiply $2$ by $- 1$ .

$y < - 2 x$

Step 2

Solve $4 x + 3 y < - 4 x + 6$ for $y$ .

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Subtract $4 x$ from $- 4 x$ .

$3 y < - 8 x + 6$

Step 2.2

Divide each term in $3 y < - 8 x + 6$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 y < - 8 x + 6$ by $3$ .

$\frac{3 y}{3} < \frac{- 8 x}{3} + \frac{6}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} < \frac{- 8 x}{3} + \frac{6}{3}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{- 8 x}{3} + \frac{6}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Move the negative in front of the fraction.

$y < - \frac{8 x}{3} + \frac{6}{3}$

Step 2.2.3.1.2

Divide $6$ by $3$ .

$y < - \frac{8 x}{3} + 2$

Step 3

Find the intersection of $y < - 2 x$ and $y < - \frac{8 x}{3} + 2$ .

$y < N o (Min i m u m)$

Step 4