Finite Math Examples

y > 6 x - 2

$y > 6 x - 2$ ,

y < - 3 x + 4

$y < - 3 x + 4$

Step 1

Simplify the first inequality.

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Step 1.1

Rewrite so

x

$x$ is on the left side of the inequality.

6 x - 2 < y

$6 x - 2 < y$ and

y < - 3 x + 4

$y < - 3 x + 4$

Step 1.2

Add

2

$2$ to both sides of the inequality.

6 x < y + 2

$6 x < y + 2$ and

y < - 3 x + 4

$y < - 3 x + 4$

Step 1.3

Divide each term in

6 x < y + 2

$6 x < y + 2$ by

6

$6$ and simplify.

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Step 1.3.1

Divide each term in

6 x < y + 2

$6 x < y + 2$ by

6

$6$ .

\frac{6 x}{6} < \frac{y}{6} + \frac{2}{6}

$\frac{6 x}{6} < \frac{y}{6} + \frac{2}{6}$ and

y < - 3 x + 4

$y < - 3 x + 4$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

6

$6$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} < \frac{y}{6} + \frac{2}{6}$ and

$y < - 3 x + 4$

Step 1.3.2.1.2

Divide

$x$ by

$1$ .

$x < \frac{y}{6} + \frac{2}{6}$ and

$y < - 3 x + 4$

$x < \frac{y}{6} + \frac{2}{6}$ and

$y < - 3 x + 4$

$x < \frac{y}{6} + \frac{2}{6}$ and

$y < - 3 x + 4$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Cancel the common factor of

$2$ and

$6$ .

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Step 1.3.3.1.1

Factor

$2$ out of

$2$ .

$x < \frac{y}{6} + \frac{2 (1)}{6}$ and

$y < - 3 x + 4$

Step 1.3.3.1.2

Cancel the common factors.

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Step 1.3.3.1.2.1

Factor

$2$ out of

$6$ .

$x < \frac{y}{6} + \frac{2 \cdot 1}{2 \cdot 3}$ and

$y < - 3 x + 4$

Step 1.3.3.1.2.2

Cancel the common factor.

$x < \frac{y}{6} + \frac{2 \cdot 1}{2 \cdot 3}$ and

$y < - 3 x + 4$

Step 1.3.3.1.2.3

Rewrite the expression.

$x < \frac{y}{6} + \frac{1}{3}$ and

$y < - 3 x + 4$

$x < \frac{y}{6} + \frac{1}{3}$ and

$y < - 3 x + 4$

$x < \frac{y}{6} + \frac{1}{3}$ and

$y < - 3 x + 4$

$x < \frac{y}{6} + \frac{1}{3}$ and

$y < - 3 x + 4$

$x < \frac{y}{6} + \frac{1}{3}$ and

$y < - 3 x + 4$

$x < \frac{y}{6} + \frac{1}{3}$ and

$y < - 3 x + 4$

Step 2

Simplify the second inequality.

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Step 2.1

Rewrite so

$x$ is on the left side of the inequality.

$x < \frac{y}{6} + \frac{1}{3}$ and

$- 3 x + 4 > y$

Step 2.2

Subtract

$4$ from both sides of the inequality.

$x < \frac{y}{6} + \frac{1}{3}$ and

$- 3 x > y - 4$

Step 2.3

Divide each term in

$- 3 x > y - 4$ by

$- 3$ and simplify.

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Step 2.3.1

Divide each term in

$- 3 x > y - 4$ by

$- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < \frac{y}{6} + \frac{1}{3}$ and

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of

$- 3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$x < \frac{y}{6} + \frac{1}{3}$ and

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

Step 2.3.2.1.2

Divide

$x$ by

$1$ .

$x < \frac{y}{6} + \frac{1}{3}$ and

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

$x < \frac{y}{6} + \frac{1}{3}$ and

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

$x < \frac{y}{6} + \frac{1}{3}$ and

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Move the negative in front of the fraction.

$x < \frac{y}{6} + \frac{1}{3}$ and

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

Step 2.3.3.1.2

Dividing two negative values results in a positive value.

$x < \frac{y}{6} + \frac{1}{3}$ and

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

$x < \frac{y}{6} + \frac{1}{3}$ and

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

$x < \frac{y}{6} + \frac{1}{3}$ and

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

$x < \frac{y}{6} + \frac{1}{3}$ and

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

$x < \frac{y}{6} + \frac{1}{3}$ and

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

Step 3