Solve the Inequality for m m+1/5<-1 2/3

$m + \frac{1}{5} < - 1 \frac{2}{3}$

Step 1

Simplify the right side.

Convert $1 \frac{2}{3}$ to an improper fraction.

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

$m + \frac{1}{5} < - (1 + \frac{2}{3})$

Add $1$ and $\frac{2}{3}$ .

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

$m + \frac{1}{5} < - (\frac{3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$m + \frac{1}{5} < - \frac{3 + 2}{3}$

Add $3$ and $2$ .

$m + \frac{1}{5} < - \frac{5}{3}$

Step 2

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

Subtract $\frac{1}{5}$ from both sides of the inequality.

$m < - \frac{5}{3} - \frac{1}{5}$

To write $- \frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$m < - \frac{5}{3} \cdot \frac{5}{5} - \frac{1}{5}$

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$m < - \frac{5}{3} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{3}{3}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{3}$ by $\frac{5}{5}$ .

$m < - \frac{5 \cdot 5}{3 \cdot 5} - \frac{1}{5} \cdot \frac{3}{3}$

Multiply $3$ by $5$ .

$m < - \frac{5 \cdot 5}{15} - \frac{1}{5} \cdot \frac{3}{3}$

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$m < - \frac{5 \cdot 5}{15} - \frac{3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$m < - \frac{5 \cdot 5}{15} - \frac{3}{15}$

Combine the numerators over the common denominator.

$m < \frac{- 5 \cdot 5 - 3}{15}$

Simplify the numerator.

Multiply $- 5$ by $5$ .

$m < \frac{- 25 - 3}{15}$

Subtract $3$ from $- 25$ .

$m < \frac{- 28}{15}$

Move the negative in front of the fraction.

$m < - \frac{28}{15}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$m < - \frac{28}{15}$

Interval Notation:

$(- \infty, - \frac{28}{15})$

Step 4

Solve the Inequality for m m+1/5<-1 2/3

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