Precalculus Examples

$2 x + 3 y > 3$ , $3 x - y < 25$

Step 1

Simplify the first inequality.

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Step 1.1

Subtract $3 y$ from both sides of the inequality.

$2 x > 3 - 3 y$ or $3 x - y < 25$

Step 1.2

Divide each term in $2 x > 3 - 3 y$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x > 3 - 3 y$ by $2$ .

$\frac{2 x}{2} > \frac{3}{2} + \frac{- 3 y}{2}$ or $3 x - y < 25$

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.

$\frac{2 x}{2} > \frac{3}{2} + \frac{- 3 y}{2}$ or $3 x - y < 25$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{3}{2} + \frac{- 3 y}{2}$ or $3 x - y < 25$

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.

$x > \frac{3}{2} - \frac{3 y}{2}$ or $3 x - y < 25$

Step 2

Simplify the second inequality.

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Step 2.1

Add $y$ to both sides of the inequality.

$x > \frac{3}{2} - \frac{3 y}{2}$ or $3 x < 25 + y$

Step 2.2

Divide each term in $3 x < 25 + y$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x < 25 + y$ by $3$ .

$x > \frac{3}{2} - \frac{3 y}{2}$ or $\frac{3 x}{3} < \frac{25}{3} + \frac{y}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x > \frac{3}{2} - \frac{3 y}{2}$ or $\frac{3 x}{3} < \frac{25}{3} + \frac{y}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{3}{2} - \frac{3 y}{2}$ or $x < \frac{25}{3} + \frac{y}{3}$

Step 3