Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

Tap for more steps...

Step 1.4.1

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

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

Step 1.4.2

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

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

Step 1.5

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.5.1

Factor $5$ out of $10$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

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.

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$0 + 2 < 2$

Step 3.2.2

Add $0$ and $2$ .

$2 < 2$

Step 4

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

No solution