# How do you solve 3/4 - 2/3>x/6?

May 26, 2018

$x < \frac{1}{2}$

#### Explanation:

$\frac{3}{4} - \frac{2}{3} > \frac{x}{6}$

You can solve this with fractions but I always recommend we turn them into integers to make everything WAY easier:

To do that we need a common denominator of $4 , 3 \mathmr{and} 6$

prime factors:

$4 = 2 \cdot 2$
$3 = 3$
$6 = 2 \cdot 3$

so the common factors in all three terns are: $2 \cdot 2 \cdot 3 = 12$

so here is the trick, we multiply 12 by both sides of the inequality like so:

$12 \left(\frac{3}{4} - \frac{2}{3}\right) > 12 \cdot \left(\frac{x}{6}\right)$

remember $12 = \frac{12}{1}$

$\left(\frac{12}{1} \cdot \frac{3}{4}\right) - \left(\frac{12}{1} \cdot \frac{2}{3}\right) > \left(\frac{12}{1} \cdot \frac{x}{6}\right)$

then cross divide:

$\left(\frac{3}{1} \cdot \frac{3}{1}\right) - \left(\frac{4}{1} \cdot \frac{2}{1}\right) > \left(\frac{2}{1} \cdot \frac{x}{1}\right)$

$\left(3 \cdot 3\right) - \left(4 \cdot 2\right) > \left(2 \cdot x\right)$

$9 - 8 > 2 x$

Now it is super simple to solve:

$9 - 8 > 2 x$

$1 > 2 x$

$\frac{1}{2} > x$

$x < \frac{1}{2}$