Algebra Examples

$\frac{3 m}{5} < - \frac{3}{20}$

Step 1

Multiply both sides by $5$ .

$\frac{3 m}{5} \cdot 5 < - \frac{3}{20} \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{3 m}{5} \cdot 5 < - \frac{3}{20} \cdot 5$

Step 2.1.1.2

Rewrite the expression.

$3 m < - \frac{3}{20} \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{3}{20} \cdot 5$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{3}{20}$ into the numerator.

$3 m < \frac{- 3}{20} \cdot 5$

Step 2.2.1.1.2

Factor $5$ out of $20$ .

$3 m < \frac{- 3}{5 (4)} \cdot 5$

Step 2.2.1.1.3

Cancel the common factor.

$3 m < \frac{- 3}{5 \cdot 4} \cdot 5$

Step 2.2.1.1.4

Rewrite the expression.

$3 m < \frac{- 3}{4}$

Step 2.2.1.2

Move the negative in front of the fraction.

$3 m < - \frac{3}{4}$

Step 3

Divide each term in $3 m < - \frac{3}{4}$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 m < - \frac{3}{4}$ by $3$ .

$\frac{3 m}{3} < \frac{- \frac{3}{4}}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 m}{3} < \frac{- \frac{3}{4}}{3}$

Step 3.2.1.2

Divide $m$ by $1$ .

$m < \frac{- \frac{3}{4}}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$m < - \frac{3}{4} \cdot \frac{1}{3}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

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

$m < \frac{- 3}{4} \cdot \frac{1}{3}$

Step 3.3.2.2

Factor $3$ out of $- 3$ .

$m < \frac{3 (- 1)}{4} \cdot \frac{1}{3}$

Step 3.3.2.3

Cancel the common factor.

$m < \frac{3 \cdot - 1}{4} \cdot \frac{1}{3}$

Step 3.3.2.4

Rewrite the expression.

$m < \frac{- 1}{4}$

Step 3.3.3

Move the negative in front of the fraction.

$m < - \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m < - \frac{1}{4}$

Interval Notation:

$(- \infty, - \frac{1}{4})$