# How do you solve for x: 12/x+3/4=3/2?

$x = 16$

#### Explanation:

Solution 1.

By inspection of the equation $\frac{12}{x} + \frac{3}{4} = \frac{3}{2}$

We know that $\frac{3}{4} + \frac{3}{4} = \frac{3}{2}$, and $\frac{12}{16} = \frac{3}{4}$.
Therefore, $x = 16$

Solution 2.

By Algebraic procedure

$\frac{12}{x} + \frac{3}{4} = \frac{3}{2}$

Multiply both sides of the equation by $x$

$x \left(\frac{12}{x} + \frac{3}{4}\right) = \left(\frac{3}{2}\right) x$

$12 + \frac{3 x}{4} = \frac{3 x}{2}$

$12 = \frac{3 x}{2} - \frac{3 x}{4}$

$12 = \frac{6 x - 3 x}{4}$

$12 = \frac{3 x}{4}$

$x = \frac{12 \cdot 4}{3}$

$x = 16$

God bless....I hope the explanation is useful.

Jul 16, 2016

$x = 16$

#### Explanation:

In an equation which has fractions, we can get rid of the denominators by multiplying all the terms by the LCM of the denominators.

$\frac{12}{x} + \frac{3}{4} = \frac{3}{2} \text{ LCM } = \textcolor{m a \ge n t a}{4 x}$

$\frac{\textcolor{m a \ge n t a}{4 x} \times 12}{x} + \frac{\textcolor{m a \ge n t a}{4 x} \times 3}{4} = \frac{3 \times \textcolor{m a \ge n t a}{4 x}}{2}$

(color(magenta)(4cancelx)xx12)/cancelx+(color(magenta)(cancel4x)xx3)/cancel4=(3xxcolor(magenta)(cancel4^2x))/cancel2color(magenta)

$48 + 3 x = 6 x$

$48 = 3 x$
$x = 16$