Algebra Examples

$4 x + 5 y \geq - 6$ $- 2 x + 7 y \geq 20$

Step 1

Solve $4 x + 5 y \geq - 6$ for $y$ .

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Step 1.1

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

$5 y \geq - 6 - 4 x$

Step 1.2

Divide each term in $5 y \geq - 6 - 4 x$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 y \geq - 6 - 4 x$ by $5$ .

$\frac{5 y}{5} \geq \frac{- 6}{5} + \frac{- 4 x}{5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} \geq \frac{- 6}{5} + \frac{- 4 x}{5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{- 6}{5} + \frac{- 4 x}{5}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$y \geq - \frac{6}{5} + \frac{- 4 x}{5}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y \geq - \frac{6}{5} - \frac{4 x}{5}$

Step 2

Solve $- 2 x + 7 y \geq 20$ for $y$ .

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Step 2.1

Add $2 x$ to both sides of the inequality.

$7 y \geq 20 + 2 x$

Step 2.2

Divide each term in $7 y \geq 20 + 2 x$ by $7$ and simplify.

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Step 2.2.1

Divide each term in $7 y \geq 20 + 2 x$ by $7$ .

$\frac{7 y}{7} \geq \frac{20}{7} + \frac{2 x}{7}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $7$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{7 y}{7} \geq \frac{20}{7} + \frac{2 x}{7}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{20}{7} + \frac{2 x}{7}$

Step 3

Find the intersection of $y \geq - \frac{6}{5} - \frac{4 x}{5}$ and $y \geq \frac{20}{7} + \frac{2 x}{7}$ .

$y \geq - \frac{6}{5} - \frac{4 x}{5}$ and $y \geq \frac{20}{7} + \frac{2 x}{7}$

Step 4