Algebra Examples

$2 x + 4 y \leq 6$ $y \geq 2$

Step 1

Solve $2 x + 4 y \leq 6$ for $y$ .

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Step 1.1

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

$4 y \leq 6 - 2 x$

Step 1.2

Divide each term in $4 y \leq 6 - 2 x$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 y \leq 6 - 2 x$ by $4$ .

$\frac{4 y}{4} \leq \frac{6}{4} + \frac{- 2 x}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} \leq \frac{6}{4} + \frac{- 2 x}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{6}{4} + \frac{- 2 x}{4}$

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

Cancel the common factor of $6$ and $4$ .

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Step 1.2.3.1.1.1

Factor $2$ out of $6$ .

$y \leq \frac{2 (3)}{4} + \frac{- 2 x}{4}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $4$ .

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

Step 1.2.3.1.1.2.2

Cancel the common factor.

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

Step 1.2.3.1.1.2.3

Rewrite the expression.

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

Step 1.2.3.1.2

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

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Step 1.2.3.1.2.1

Factor $2$ out of $- 2 x$ .

$y \leq \frac{3}{2} + \frac{2 (- x)}{4}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $4$ .

$y \leq \frac{3}{2} + \frac{2 (- x)}{2 (2)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y \leq \frac{3}{2} + \frac{2 (- x)}{2 \cdot 2}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y \leq \frac{3}{2} + \frac{- x}{2}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y \leq \frac{3}{2} - \frac{x}{2}$

Step 2

Find the intersection of $y \leq \frac{3}{2} - \frac{x}{2}$ and $y \geq 2$ .

$2 \leq y \leq \frac{3}{2} - \frac{x}{2}$

Step 3