Solve the Inequality for m m+1/3<-2 1/4

$m + \frac{1}{3} < - 2 \frac{1}{4}$

Simplify the right side.

Convert $2 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$m + \frac{1}{3} < - (2 + \frac{1}{4})$

Add $2$ and $\frac{1}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$m + \frac{1}{3} < - (2 \cdot \frac{4}{4} + \frac{1}{4})$

Combine $2$ and $\frac{4}{4}$ .

$m + \frac{1}{3} < - (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$m + \frac{1}{3} < - \frac{2 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$m + \frac{1}{3} < - \frac{8 + 1}{4}$

Add $8$ and $1$ .

$m + \frac{1}{3} < - \frac{9}{4}$

Move all terms not containing $m$ to the right side of the inequality.

Subtract $\frac{1}{3}$ from both sides of the inequality.

$m < - \frac{9}{4} - \frac{1}{3}$

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$m < - \frac{9}{4} \cdot \frac{3}{3} - \frac{1}{3}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$m < - \frac{9}{4} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{4}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{4}$ by $\frac{3}{3}$ .

$m < - \frac{9 \cdot 3}{4 \cdot 3} - \frac{1}{3} \cdot \frac{4}{4}$

Multiply $4$ by $3$ .

$m < - \frac{9 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$m < - \frac{9 \cdot 3}{12} - \frac{4}{3 \cdot 4}$

Multiply $3$ by $4$ .

$m < - \frac{9 \cdot 3}{12} - \frac{4}{12}$

Combine the numerators over the common denominator.

$m < \frac{- 9 \cdot 3 - 4}{12}$

Simplify the numerator.

Multiply $- 9$ by $3$ .

$m < \frac{- 27 - 4}{12}$

Subtract $4$ from $- 27$ .

$m < \frac{- 31}{12}$

Move the negative in front of the fraction.

$m < - \frac{31}{12}$

The result can be shown in multiple forms.

Inequality Form:

$m < - \frac{31}{12}$

Interval Notation:

$(- \infty, - \frac{31}{12})$

Solve the Inequality for m m+1/3<-2 1/4

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