Trigonometry Examples

$\frac{- 10}{x} = \frac{- 16}{x + 3}$

Step 1

Simplify both sides.

Tap for more steps...

Step 1.1

Move the negative in front of the fraction.

$- \frac{10}{x} = \frac{- 16}{x + 3}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{10}{x} = - \frac{16}{x + 3}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$- 10 (x + 3) = x \cdot - 16$

Step 3

Solve the equation for $x$ .

Tap for more steps...

Step 3.1

Simplify $- 10 (x + 3)$ .

Tap for more steps...

Step 3.1.1

Rewrite.

$0 + 0 - 10 (x + 3) = x \cdot - 16$

Step 3.1.2

Simplify by adding zeros.

$- 10 (x + 3) = x \cdot - 16$

Step 3.1.3

Apply the distributive property.

$- 10 x - 10 \cdot 3 = x \cdot - 16$

Step 3.1.4

Multiply $- 10$ by $3$ .

$- 10 x - 30 = x \cdot - 16$

Step 3.2

Move $- 16$ to the left of $x$ .

$- 10 x - 30 = - 16 x$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Add $16 x$ to both sides of the equation.

$- 10 x - 30 + 16 x = 0$

Step 3.3.2

Add $- 10 x$ and $16 x$ .

$6 x - 30 = 0$

Step 3.4

Add $30$ to both sides of the equation.

$6 x = 30$

Step 3.5

Divide each term in $6 x = 30$ by $6$ and simplify.

Tap for more steps...

Step 3.5.1

Divide each term in $6 x = 30$ by $6$ .

$\frac{6 x}{6} = \frac{30}{6}$

Step 3.5.2

Simplify the left side.

Tap for more steps...

Step 3.5.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.5.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{30}{6}$

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{6}$

Step 3.5.3

Simplify the right side.

Tap for more steps...

Step 3.5.3.1

Divide $30$ by $6$ .

$x = 5$