Algebra Examples

$\frac{- 8}{x + 6} = \frac{3}{2 x}$

Step 1

Move the negative in front of the fraction.

$- \frac{8}{x + 6} = \frac{3}{2 x}$

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.

$- 8 (2 x) = (x + 6) \cdot 3$

Step 3

Solve the equation for $x$ .

Tap for more steps...

Step 3.1

Multiply $2$ by $- 8$ .

$- 16 x = (x + 6) \cdot 3$

Step 3.2

Simplify $(x + 6) \cdot 3$ .

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$- 16 x = x \cdot 3 + 6 \cdot 3$

Step 3.2.2

Simplify the expression.

Tap for more steps...

Step 3.2.2.1

Move $3$ to the left of $x$ .

$- 16 x = 3 \cdot x + 6 \cdot 3$

Step 3.2.2.2

Multiply $6$ by $3$ .

$- 16 x = 3 x + 18$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Subtract $3 x$ from both sides of the equation.

$- 16 x - 3 x = 18$

Step 3.3.2

Subtract $3 x$ from $- 16 x$ .

$- 19 x = 18$

Step 3.4

Divide each term in $- 19 x = 18$ by $- 19$ and simplify.

Tap for more steps...

Step 3.4.1

Divide each term in $- 19 x = 18$ by $- 19$ .

$\frac{- 19 x}{- 19} = \frac{18}{- 19}$

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Cancel the common factor of $- 19$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor.

$\frac{- 19 x}{- 19} = \frac{18}{- 19}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{- 19}$

Step 3.4.3

Simplify the right side.

Tap for more steps...

Step 3.4.3.1

Move the negative in front of the fraction.

$x = - \frac{18}{19}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{18}{19}$

Decimal Form:

$x = - 0.94736842 \dots$