Solve for m m+1/4<-1 2/5

$m + \frac{1}{4} < - 1 \frac{2}{5}$

Step 1

Simplify the right side.

Convert $1 \frac{2}{5}$ to an improper fraction.

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

$m + \frac{1}{4} < - (1 + \frac{2}{5})$

Add $1$ and $\frac{2}{5}$ .

Write $1$ as a fraction with a common denominator.

$m + \frac{1}{4} < - (\frac{5}{5} + \frac{2}{5})$

Combine the numerators over the common denominator.

$m + \frac{1}{4} < - \frac{5 + 2}{5}$

Add $5$ and $2$ .

$m + \frac{1}{4} < - \frac{7}{5}$

Step 2

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

Subtract $\frac{1}{4}$ from both sides of the inequality.

$m < - \frac{7}{5} - \frac{1}{4}$

To write $- \frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$m < - \frac{7}{5} \cdot \frac{4}{4} - \frac{1}{4}$

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$m < - \frac{7}{5} \cdot \frac{4}{4} - \frac{1}{4} \cdot \frac{5}{5}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{5}$ by $\frac{4}{4}$ .

$m < - \frac{7 \cdot 4}{5 \cdot 4} - \frac{1}{4} \cdot \frac{5}{5}$

Multiply $5$ by $4$ .

$m < - \frac{7 \cdot 4}{20} - \frac{1}{4} \cdot \frac{5}{5}$

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$m < - \frac{7 \cdot 4}{20} - \frac{5}{4 \cdot 5}$

Multiply $4$ by $5$ .

$m < - \frac{7 \cdot 4}{20} - \frac{5}{20}$

Combine the numerators over the common denominator.

$m < \frac{- 7 \cdot 4 - 5}{20}$

Simplify the numerator.

Multiply $- 7$ by $4$ .

$m < \frac{- 28 - 5}{20}$

Subtract $5$ from $- 28$ .

$m < \frac{- 33}{20}$

Move the negative in front of the fraction.

$m < - \frac{33}{20}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$m < - \frac{33}{20}$

Interval Notation:

$(- \infty, - \frac{33}{20})$