Algebra Examples

$x + y \geq 3$ $x + 2 y \geq 5$

Step 1

Subtract $x$ from both sides of the inequality.

$y \geq 3 - x$

Step 2

Solve $x + 2 y \geq 5$ for $y$ .

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Step 2.1

Subtract $x$ from both sides of the inequality.

$2 y \geq 5 - x$

Step 2.2

Divide each term in $2 y \geq 5 - x$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 y \geq 5 - x$ by $2$ .

$\frac{2 y}{2} \geq \frac{5}{2} + \frac{- x}{2}$

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.

$\frac{2 y}{2} \geq \frac{5}{2} + \frac{- x}{2}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{5}{2} + \frac{- x}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move the negative in front of the fraction.

$y \geq \frac{5}{2} - \frac{x}{2}$

Step 3

Find the intersection of $y \geq 3 - x$ and $y \geq \frac{5}{2} - \frac{x}{2}$ .

$y \geq 3 - x$ and $y \geq \frac{5}{2} - \frac{x}{2}$

Step 4