# How do you solve 3= \frac { 5x - 4} { 3} + \frac { 3x - 1} { 5}?

##### 2 Answers
Jan 16, 2018

$x = 2$

#### Explanation:

$3 = \frac{5 x - 4}{3} + \frac{3 x - 1}{5}$

Multiply all terms by the LCM of $3$ and $5$ which is $15$.

$3 \times 15 = 15 \times \frac{5 x - 4}{3} + 15 \times \frac{3 x - 1}{5}$

$45 = 5 \cancel{15} \times \frac{5 x - 4}{1 \cancel{3}} + 3 \cancel{15} \times \frac{3 x - 1}{1 \cancel{5}}$

$45 = 5 \left(5 x - 4\right) + 3 \left(3 x - 1\right)$

Open the brackets and simplify.

$45 = 25 x - 20 + 9 x - 3$

$45 = 25 x + 9 x - 20 - 3$

$45 = \left(25 x + 9 x\right) - \left(20 + 3\right)$

$45 = 34 x - 23$

Add $23$ to both sides.

$45 + 23 = 34 x - 23 + 23$

$68 = 34 x$

Divide both sides by $34$.

$\frac{68}{34} = \frac{34 x}{34}$

$\frac{2 \cancel{68}}{1 \cancel{34}} = \frac{\cancel{34} x}{\cancel{34}}$

$2 = x$ or $x = 2$

Jan 16, 2018

Please see the step process below;

#### Explanation:

$3 = \setminus \frac{5 x - 4}{3} + \setminus \frac{3 x - 1}{5}$

First Step: Multiply via the LCM, in this case the LCM $= 15$

$15 \left(\frac{3}{1}\right) = 15 \left(\frac{5 x - 4}{3}\right) + 15 \left(\frac{3 x - 1}{5}\right)$

Second Step: Simplify

$15 \left(\frac{3}{1}\right) = {\cancel{15}}^{5} \left(\frac{5 x - 4}{\cancel{3}}\right) + {\cancel{15}}^{3} \left(\frac{3 x - 1}{\cancel{5}}\right)$

$15 \left(3\right) = 5 \left(5 x - 4\right) + 3 \left(3 x - 1\right)$

$45 = 25 x - 20 + 9 x - 3$

Third Step: Collecting like terms

$45 = 25 x + 9 x - 20 - 3$

$45 = 34 x - 23$

$45 + 23 = 34 x$

$68 = 34 x$

Divide both sides by $34$

$\frac{68}{34} = \frac{34 x}{34}$

$\frac{68}{34} = \frac{\cancel{34} x}{\cancel{34}}$

$\frac{68}{34} = x$

$x = 2$