# 3/4x -1/3 =5 What is x?

Nov 17, 2017

$x = \frac{64}{9}$

#### Explanation:

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

1) Start by clearing the first fraction by multiplying all the terms on both sides by 4 and letting that denominator cancel.
After you have multiplied and canceled, you will get this:
$3 x - \left(\frac{4}{3}\right) = 20$

2) Next, clear the other fraction by multiplying all the terms on both sides by 3 and letting that denominator cancel.
After you have multiplied and canceled, you will have this:
$9 x - 4 = 60$

3) Add 4 to both sides to isolate the $9 x$ term
$9 x = 64$

4) Divide both sides by 9 to isolate $x$
$x = \frac{64}{9}$ <-- answer
........................

Check

1) Sub in $\frac{64}{9}$ for $x$ in the original equation

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

$\left(\frac{3}{4}\right) \left(\frac{64}{9}\right) - \left(\frac{1}{3}\right)$ should still equal 5

2) Reduce the fractions to lowest terms

$\left({\cancel{3}}^{1} / \left({\cancel{4}}^{1}\right)\right) \left(\frac{{\cancel{64}}^{16}}{{\cancel{9}}^{3}}\right) - \left(\frac{1}{3}\right)$

$\frac{16}{3} - \frac{1}{3}$

3) Subtract the fractions.
They already have a common denominator.

$\frac{15}{3}$
This should still equal 5 after you change it to a whole number

4) 5 does equal 5
Check!