Trigonometry Examples

$\frac{4}{5} x > 3 (\frac{1}{5} x - 1) + 4$

Step 1

Simplify $\frac{4}{5} x$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{4}{5} x > 3 (\frac{1}{5} x - 1) + 4$

Step 1.2

Simplify by adding zeros.

$\frac{4}{5} x > 3 (\frac{1}{5} x - 1) + 4$

Step 1.3

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

$\frac{4 x}{5} > 3 (\frac{1}{5} x - 1) + 4$

Step 2

Simplify $3 (\frac{1}{5} x - 1) + 4$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

$\frac{4 x}{5} > 3 (\frac{x}{5} - 1) + 4$

Step 2.1.2

Apply the distributive property.

$\frac{4 x}{5} > 3 \frac{x}{5} + 3 \cdot - 1 + 4$

Step 2.1.3

Combine $3$ and $\frac{x}{5}$ .

$\frac{4 x}{5} > \frac{3 x}{5} + 3 \cdot - 1 + 4$

Step 2.1.4

Multiply $3$ by $- 1$ .

$\frac{4 x}{5} > \frac{3 x}{5} - 3 + 4$

Step 2.2

Add $- 3$ and $4$ .

$\frac{4 x}{5} > \frac{3 x}{5} + 1$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{3 x}{5}$ from both sides of the inequality.

$\frac{4 x}{5} - \frac{3 x}{5} > 1$

Step 3.2

Combine the numerators over the common denominator.

$\frac{4 x - 3 x}{5} > 1$

Step 3.3

Subtract $3 x$ from $4 x$ .

$\frac{x}{5} > 1$

Step 4

Multiply both sides by $5$ .

$\frac{x}{5} \cdot 5 > 1 \cdot 5$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor.

$\frac{x}{5} \cdot 5 > 1 \cdot 5$

Step 5.1.1.2

Rewrite the expression.

$x > 1 \cdot 5$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $5$ by $1$ .

$x > 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 5$

Interval Notation:

$(5, \infty)$