Finite Math Examples

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

Step 1

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

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

Step 2

Multiply each term in $- \frac{3}{4} x < y$ by $- \frac{4}{3}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $- \frac{3}{4} x < y$ by $- \frac{4}{3}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{3}{4} x (- \frac{4}{3}) > y (- \frac{4}{3})$

Step 2.2

Simplify the left side.

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Step 2.2.1

Combine $x$ and $\frac{3}{4}$ .

$- \frac{x \cdot 3}{4} (- \frac{4}{3}) > y (- \frac{4}{3})$

Step 2.2.2

Cancel the common factor of $3$ .

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Step 2.2.2.1

Move the leading negative in $- \frac{x \cdot 3}{4}$ into the numerator.

$\frac{- x \cdot 3}{4} (- \frac{4}{3}) > y (- \frac{4}{3})$

Step 2.2.2.2

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- x \cdot 3}{4} \cdot \frac{- 4}{3} > y (- \frac{4}{3})$

Step 2.2.2.3

Factor $3$ out of $- x \cdot 3$ .

$\frac{3 \cdot (- x)}{4} \cdot \frac{- 4}{3} > y (- \frac{4}{3})$

Step 2.2.2.4

Cancel the common factor.

$\frac{3 \cdot (- x)}{4} \cdot \frac{- 4}{3} > y (- \frac{4}{3})$

Step 2.2.2.5

Rewrite the expression.

$\frac{- x}{4} \cdot - 4 > y (- \frac{4}{3})$

Step 2.2.3

Cancel the common factor of $4$ .

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Step 2.2.3.1

Factor $4$ out of $- 4$ .

$\frac{- x}{4} \cdot (4 (- 1)) > y (- \frac{4}{3})$

Step 2.2.3.2

Cancel the common factor.

$\frac{- x}{4} \cdot (4 \cdot - 1) > y (- \frac{4}{3})$

Step 2.2.3.3

Rewrite the expression.

$- x \cdot - 1 > y (- \frac{4}{3})$

Step 2.2.4

Multiply.

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Step 2.2.4.1

Multiply $- 1$ by $- 1$ .

$1 x > y (- \frac{4}{3})$

Step 2.2.4.2

Multiply $x$ by $1$ .

$x > y (- \frac{4}{3})$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine $y$ and $\frac{4}{3}$ .

$x > - \frac{y \cdot 4}{3}$

Step 2.3.2

Move $4$ to the left of $y$ .

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