Pre-Algebra Examples

$5 x + 2 y < 10$ , $x - 2 y > 2$

Step 1

Solve $5 x + 2 y < 10$ for $y$ .

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Step 1.1

Subtract $5 x$ from both sides of the inequality.

$2 y < 10 - 5 x$

Step 1.2

Divide each term in $2 y < 10 - 5 x$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y < 10 - 5 x$ by $2$ .

$\frac{2 y}{2} < \frac{10}{2} + \frac{- 5 x}{2}$

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.

$\frac{2 y}{2} < \frac{10}{2} + \frac{- 5 x}{2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{10}{2} + \frac{- 5 x}{2}$

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

Divide $10$ by $2$ .

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

Step 1.2.3.1.2

Move the negative in front of the fraction.

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

Step 2

Solve $x - 2 y > 2$ for $y$ .

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Step 2.1

Subtract $x$ from both sides of the inequality.

$- 2 y > 2 - x$

Step 2.2

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

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Step 2.2.1

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

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

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.

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

Step 2.2.2.1.2

Divide $y$ by $1$ .

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

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 $- 2$ .

$y < - 1 + \frac{- x}{- 2}$

Step 2.2.3.1.2

Dividing two negative values results in a positive value.

$y < - 1 + \frac{x}{2}$

Step 3

Find the intersection of $y < 5 - \frac{5 x}{2}$ and $y < - 1 + \frac{x}{2}$ .

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

Step 4