Trigonometry Examples

$4 (3 x + 5) = \frac{1}{256}$

Step 1

Divide each term in $4 (3 x + 5) = \frac{1}{256}$ by $4$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $4 (3 x + 5) = \frac{1}{256}$ by $4$ .

$\frac{4 (3 x + 5)}{4} = \frac{\frac{1}{256}}{4}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{4 (3 x + 5)}{4} = \frac{\frac{1}{256}}{4}$

Step 1.2.1.2

Divide $3 x + 5$ by $1$ .

$3 x + 5 = \frac{\frac{1}{256}}{4}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Multiply the numerator by the reciprocal of the denominator.

$3 x + 5 = \frac{1}{256} \cdot \frac{1}{4}$

Step 1.3.2

Multiply $\frac{1}{256} \cdot \frac{1}{4}$ .

Tap for more steps...

Step 1.3.2.1

Multiply $\frac{1}{256}$ by $\frac{1}{4}$ .

$3 x + 5 = \frac{1}{256 \cdot 4}$

Step 1.3.2.2

Multiply $256$ by $4$ .

$3 x + 5 = \frac{1}{1024}$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $5$ from both sides of the equation.

$3 x = \frac{1}{1024} - 5$

Step 2.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{1024}{1024}$ .

$3 x = \frac{1}{1024} - 5 \cdot \frac{1024}{1024}$

Step 2.3

Combine $- 5$ and $\frac{1024}{1024}$ .

$3 x = \frac{1}{1024} + \frac{- 5 \cdot 1024}{1024}$

Step 2.4

Combine the numerators over the common denominator.

$3 x = \frac{1 - 5 \cdot 1024}{1024}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $- 5$ by $1024$ .

$3 x = \frac{1 - 5120}{1024}$

Step 2.5.2

Subtract $5120$ from $1$ .

$3 x = \frac{- 5119}{1024}$

Step 2.6

Move the negative in front of the fraction.

$3 x = - \frac{5119}{1024}$

Step 3

Divide each term in $3 x = - \frac{5119}{1024}$ by $3$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $3 x = - \frac{5119}{1024}$ by $3$ .

$\frac{3 x}{3} = \frac{- \frac{5119}{1024}}{3}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \frac{5119}{1024}}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{5119}{1024}}{3}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{5119}{1024} \cdot \frac{1}{3}$

Step 3.3.2

Multiply $- \frac{5119}{1024} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 3.3.2.1

Multiply $\frac{1}{3}$ by $\frac{5119}{1024}$ .

$x = - \frac{5119}{3 \cdot 1024}$

Step 3.3.2.2

Multiply $3$ by $1024$ .

$x = - \frac{5119}{3072}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5119}{3072}$

Decimal Form:

$x = - 1.66634114 \dots$

Mixed Number Form:

$x = - 1 \frac{2047}{3072}$