# Could any one tell me how to solve this equation? Thanks :)

Nov 10, 2016

$x = \frac{42}{55}$

#### Explanation:

$3 \frac{x}{2} + 7 \frac{2}{3} x + 2 = \frac{24}{2} - x \text{ } \leftarrow$ change to improper fractions

$\frac{6 + x}{2} + \frac{23 x}{3} + 2 = 12 - x \text{ } \leftarrow \times 6$

$\frac{{\cancel{6}}^{3} \times \left(6 + x\right)}{\cancel{2}} + \frac{{\cancel{6}}^{2} \times \left(23 x\right)}{\cancel{3}} + 6 \times 2 = 6 \times 12 - x \times 6$

$18 + 3 x + 46 x + 12 = 72 - 6 x$

$49 x + 6 x = 72 - 18 - 12$

$55 x = 42$

$x = \frac{42}{55}$