# How do you solve the inequality (4x-3)/2 - (3x-3)/3<3?

Jul 14, 2016

$\therefore x < \frac{7}{2}$

#### Explanation:

Given that, $\frac{4 x - 3}{2} - \frac{3 x - 3}{3} < 3.$

$\therefore \frac{4 x - 3}{2} - \frac{3 \left(x - 1\right)}{3} < 3$

$\therefore \frac{4 x - 3}{2} - \left(x - 1\right) < 3$

Multiplying by $2 > 0$, the order of the given inequality will not be reversed.

$\therefore 4 x - 3 - 2 \left(x - 1\right) < 6$

$\therefore 4 x - 3 - 2 x + 2 < 6$

$\therefore 2 x - 1 < 6.$

Adding $1$,

$2 x - 1 + 1 = 6 + 1$

$\therefore 2 x < 7$

Multiplying by $\frac{1}{2} > 0$

$\therefore x < \frac{7}{2}$