# How do you solve (3/2)(x+8) = 6x?

Jan 30, 2016

The solution is the usual approach to algebra with order of operations. See the explanation below. The solution is $x = \frac{8}{3}$.

#### Explanation:

We first do brackets (or parentheses), then indices (powers), then multiplication, division, addition and subtraction. This is called 'order of operations', and there are various ways to remember it.

In this case, multiply out the brackets first:

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

Simplifying and cancelling,

$\frac{3 x}{2} + 12 = 6 x$

Let's multiply everything by 2 for neatness:

$3 x + 24 = 12 x$

Subtract $3 x$ from both sides:

$24 = 9 x$

Reverse the order:

$9 x = 24$

Divide both sides by 9:

$x = \frac{24}{9} = \frac{8}{3}$

(you can check this by plugging it into the original equation and seeing if it makes it true (i.e. both sides are equal))