Pre-Algebra Examples

$4 x + 3 y < 12$ , $5 x - 2 y < 101$

Step 1

Solve $4 x + 3 y < 12$ for $y$ .

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Step 1.1

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

$3 y < 12 - 4 x$

Step 1.2

Divide each term in $3 y < 12 - 4 x$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 y < 12 - 4 x$ by $3$ .

$\frac{3 y}{3} < \frac{12}{3} + \frac{- 4 x}{3}$

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.

$\frac{3 y}{3} < \frac{12}{3} + \frac{- 4 x}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{12}{3} + \frac{- 4 x}{3}$

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 $12$ by $3$ .

$y < 4 + \frac{- 4 x}{3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y < 4 - \frac{4 x}{3}$

Step 2

Solve $5 x - 2 y < 101$ for $y$ .

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Step 2.1

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

$- 2 y < 101 - 5 x$

Step 2.2

Divide each term in $- 2 y < 101 - 5 x$ by $- 2$ and simplify.

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Step 2.2.1

Divide each term in $- 2 y < 101 - 5 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{101}{- 2} + \frac{- 5 x}{- 2}$

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.

$\frac{- 2 y}{- 2} > \frac{101}{- 2} + \frac{- 5 x}{- 2}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{101}{- 2} + \frac{- 5 x}{- 2}$

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

Move the negative in front of the fraction.

$y > - \frac{101}{2} + \frac{- 5 x}{- 2}$

Step 2.2.3.1.2

Dividing two negative values results in a positive value.

$y > - \frac{101}{2} + \frac{5 x}{2}$

Step 3

Find the intersection of $y < 4 - \frac{4 x}{3}$ and $y > - \frac{101}{2} + \frac{5 x}{2}$ .

$- \frac{101}{2} + \frac{5 x}{2} < y < 4 - \frac{4 x}{3}$

Step 4