How do you solve 2x - (3/4) + (4/3) = 8 + (4/3)?

Jun 14, 2017

$x = 4 \frac{3}{8}$

Explanation:

$2 x - \left(\frac{3}{4}\right) + \left(\frac{4}{3}\right) = 8 + \left(\frac{4}{3}\right)$

$2 x - \left(\frac{3}{4}\right) \cancel{+ \left(\frac{4}{3}\right)} = 8 \cancel{+ \left(\frac{4}{3}\right)}$

$2 x - \left(\frac{3}{4}\right) = 8$

$2 x = 8 \frac{3}{4}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\textcolor{red}{\cancel{2}}} = \frac{8 \frac{3}{4}}{2}$

x = 35/4 ÷ 2/1

$x = \frac{35}{4} \times \frac{1}{2}$

$x = \frac{35}{8}$

color(blue)(x = 4 3/8

Now we can plug in this number to prove our answer.

$2 \times 4 \frac{3}{8} - \left(\frac{3}{4}\right) + \left(\frac{4}{3}\right) = 8 + \left(\frac{4}{3}\right)$

$8 \frac{3}{4} - \left(\frac{3}{4}\right) + \left(\frac{4}{3}\right) = 8 + \left(\frac{4}{3}\right)$

$8 + \left(\frac{4}{3}\right) = 8 + \left(\frac{4}{3}\right)$

$8 \frac{4}{3} = 8 + \left(\frac{4}{3}\right)$

$\therefore 8 \frac{4}{3} = 8 \frac{4}{3}$