Finite Math Examples

$\frac{x}{- 3} < \frac{3}{5}$

Step 1

Multiply both sides by $- 3$ .

$\frac{x}{- 3} \cdot - 3 > \frac{3}{5} \cdot - 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{x}{- 3} \cdot - 3$ .

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Step 2.1.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1.1

Factor $3$ out of $- 3$ .

$\frac{x}{3 (- 1)} \cdot - 3 > \frac{3}{5} \cdot - 3$

Step 2.1.1.1.2

Factor $3$ out of $- 3$ .

$\frac{x}{3 \cdot - 1} \cdot (3 \cdot - 1) > \frac{3}{5} \cdot - 3$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{x}{3 \cdot - 1} \cdot (3 \cdot - 1) > \frac{3}{5} \cdot - 3$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{x}{- 1} \cdot - 1 > \frac{3}{5} \cdot - 3$

Step 2.1.1.2

Combine $\frac{x}{- 1}$ and $- 1$ .

$\frac{x \cdot - 1}{- 1} > \frac{3}{5} \cdot - 3$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{x \cdot - 1}{- 1}$ .

$- 1 \cdot (x \cdot - 1) > \frac{3}{5} \cdot - 3$

Step 2.1.1.3.2

Rewrite $- 1 \cdot (x \cdot - 1)$ as $- (x \cdot - 1)$ .

$- (x \cdot - 1) > \frac{3}{5} \cdot - 3$

Step 2.1.1.3.3

Move $- 1$ to the left of $x$ .

$- (- 1 \cdot x) > \frac{3}{5} \cdot - 3$

Step 2.1.1.3.4

Rewrite $- 1 x$ as $- x$ .

$- - x > \frac{3}{5} \cdot - 3$

Step 2.1.1.4

Multiply $- - x$ .

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 x > \frac{3}{5} \cdot - 3$

Step 2.1.1.4.2

Multiply $x$ by $1$ .

$x > \frac{3}{5} \cdot - 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{5} \cdot - 3$ .

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Step 2.2.1.1

Multiply $\frac{3}{5} \cdot - 3$ .

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Step 2.2.1.1.1

Combine $\frac{3}{5}$ and $- 3$ .

$x > \frac{3 \cdot - 3}{5}$

Step 2.2.1.1.2

Multiply $3$ by $- 3$ .

$x > \frac{- 9}{5}$

Step 2.2.1.2

Move the negative in front of the fraction.

$x > - \frac{9}{5}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{9}{5}$

Interval Notation:

$(- \frac{9}{5}, \infty)$