Solve the Inequality for m 1/5(4m+10)<4/5m+2

$\frac{1}{5} (4 m + 10) < \frac{4}{5} m + 2$

Step 1

Simplify $\frac{1}{5} \cdot (4 m + 10)$ .

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (4 m + 10) < \frac{4}{5} m + 2$

Simplify by adding zeros.

$\frac{1}{5} \cdot (4 m + 10) < \frac{4}{5} m + 2$

Apply the distributive property.

$\frac{1}{5} (4 m) + \frac{1}{5} \cdot 10 < \frac{4}{5} m + 2$

Multiply $\frac{1}{5} (4 m)$ .

Combine $4$ and $\frac{1}{5}$ .

$\frac{4}{5} m + \frac{1}{5} \cdot 10 < \frac{4}{5} m + 2$

Combine $\frac{4}{5}$ and $m$ .

$\frac{4 m}{5} + \frac{1}{5} \cdot 10 < \frac{4}{5} m + 2$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Combine $\frac{4}{5}$ and $m$ .

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

Step 3

Move all terms containing $m$ to the left side of the inequality.

Subtract $\frac{4 m}{5}$ from both sides of the inequality.

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

Combine the opposite terms in $\frac{4 m}{5} + 2 - \frac{4 m}{5}$ .

Subtract $\frac{4 m}{5}$ from $\frac{4 m}{5}$ .

$0 + 2 < 2$

Add $0$ and $2$ .

$2 < 2$

Step 4

Since $2 > 2$ , there are no solutions.

No solution