# Question #dbf22

##### 1 Answer
Nov 27, 2015

$x > \frac{8}{3}$

#### Explanation:

If you look at https://socratic.org/help/symbols you can find tips on formatting. Use the hash at both the start and end of any maths equations etc.

Given: $\frac{1}{4} \left(x + 4\right) < \frac{1}{5} \left(2 x + 3\right)$

Use standard manipulation as if the < behaved the same way (sort of ! ) as an =. You have to be careful about what you are doing if you have any multiplications involving negatives. You don't!

$\implies 5 \left(x + 4\right) < 4 \left(2 x + 3\right)$

$5 x + 20 < 8 x + 12$

Collecting like terms

$20 - 12 < 8 x - 5 x$

$8 < 3 x$

Divide by 3

$\frac{8}{3} < x$

Turn it round so that it has the variable on the left. Notice that you still have to make $x$ bigger than $\frac{8}{3}$ so that turns round as well.

$x > \frac{8}{3}$