# How do you solve  7/(9x)+2/3=5+1/(3x)?

Jun 21, 2017

$x = \frac{4}{39}$

#### Explanation:

to clear the denominators, multiply both sides by $9 x$

$\left(9 x\right) \left(\frac{7}{9 x}\right) = 7$;
$\left(9 x\right) \left(\frac{2}{3}\right) = 6 x$;
$\left(9 x\right) \left(5\right) = 45 x$;
$\left(9 x\right) \left(\frac{1}{3 x}\right) = 3$

you now have $7 + 6 x = 45 x + 3$

by subtracting $6 x$ and 3 from both sides, you get $39 x = 4$

divide both sides by 39

$x = \frac{4}{39}$

Jun 22, 2017

Multiply the equation by numbers that will eliminate the denominator terms.

#### Explanation:

In this case we would multiply the whole thing by 9x because that is the least value that includes factors from all of the denominators (x, 3, 9).
$\left(9 \cdot x\right) \cdot \left(\frac{7}{9 \cdot x} + \frac{2}{3} = 5 + \frac{1}{3 \cdot x}\right)$

$7 + 6 \cdot x = 45 \cdot x + 3$ ; Now we can solve for ‘x’ normally.

$4 = 39 \cdot x$ ; $x = 0.103$

CHECK:
$\frac{7}{9 \cdot 0.103} + \frac{2}{3} = 5 + \frac{1}{3 \cdot 0.103}$
$\frac{7}{0.927} + \frac{2}{3} = 5 + \frac{1}{0.309}$

$7.55 + 0.667 = 5 + 3.24$
$8.22 = 8.24$ OK, given rounding errors.