Algebra Examples

$3 x + 2 y \geq - 2 x + 2 y \leq 2$

Step 1

Solve $3 x + 2 y \geq - 2 x + 2 y$ 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 $2 y$ from both sides of the inequality.

$3 x + 2 y - 2 y \geq - 2 x$

Step 1.1.2

Combine the opposite terms in $3 x + 2 y - 2 y$ .

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Step 1.1.2.1

Subtract $2 y$ from $2 y$ .

$3 x + 0 \geq - 2 x$

Step 1.1.2.2

Add $3 x$ and $0$ .

$3 x \geq - 2 x$

Step 1.2

Divide each term in $3 x \geq - 2 x$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x \geq - 2 x$ by $3$ .

$\frac{3 x}{3} \geq \frac{- 2 x}{3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{- 2 x}{3}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 2 x}{3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$x \geq - \frac{2 x}{3}$

Step 1.3

Multiply both sides by $3$ .

$x \cdot 3 \geq - \frac{2 x}{3} \cdot 3$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Move $3$ to the left of $x$ .

$3 x \geq - \frac{2 x}{3} \cdot 3$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Cancel the common factor of $3$ .

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Step 1.4.2.1.1

Move the leading negative in $- \frac{2 x}{3}$ into the numerator.

$3 x \geq \frac{- 2 x}{3} \cdot 3$

Step 1.4.2.1.2

Cancel the common factor.

$3 x \geq \frac{- 2 x}{3} \cdot 3$

Step 1.4.2.1.3

Rewrite the expression.

$3 x \geq - 2 x$

Step 1.5

Solve for $x$ .

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Step 1.5.1

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

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Step 1.5.1.1

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

$3 x + 2 x \geq 0$

Step 1.5.1.2

Add $3 x$ and $2 x$ .

$5 x \geq 0$

Step 1.5.2

Divide each term in $5 x \geq 0$ by $5$ and simplify.

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Step 1.5.2.1

Divide each term in $5 x \geq 0$ by $5$ .

$\frac{5 x}{5} \geq \frac{0}{5}$

Step 1.5.2.2

Simplify the left side.

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Step 1.5.2.2.1

Cancel the common factor of $5$ .

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Step 1.5.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{0}{5}$

Step 1.5.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{0}{5}$

Step 1.5.2.3

Simplify the right side.

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Step 1.5.2.3.1

Divide $0$ by $5$ .

$x \geq 0$

Step 1.6

The variable $y$ got canceled.

All real numbers

Step 2

Solve $- 2 x + 2 y \leq 2$ for $y$ .

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Step 2.1

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

$2 y \leq 2 + 2 x$

Step 2.2

Divide each term in $2 y \leq 2 + 2 x$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 y \leq 2 + 2 x$ by $2$ .

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

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.1.2

Divide $y$ by $1$ .

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

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

Divide $2$ by $2$ .

$y \leq 1 + \frac{2 x}{2}$

Step 2.2.3.1.2

Cancel the common factor of $2$ .

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Step 2.2.3.1.2.1

Cancel the common factor.

$y \leq 1 + \frac{2 x}{2}$

Step 2.2.3.1.2.2

Divide $x$ by $1$ .

$y \leq 1 + x$

Step 3

Find the intersection.

$y \leq N o (Min i m u m)$

Step 4