# How do you solve \frac { 1} { 4} ( 5x + 4) - \frac { 22} { 3} = \frac { 14} { 3}?

Jun 10, 2017

$x = \frac{132}{15} \approx 8.8$

#### Explanation:

First multiply both sides by $12$. This will get rid of the fractions because $12$ is divisible by both $4$ and $3$.

$\textcolor{red}{12} \times \frac{1}{4} \left(5 x + 4\right) - \textcolor{red}{12} \times \frac{22}{3} = \textcolor{red}{12} \times \frac{14}{3}$

$3 \left(5 x + 4\right) - 4 \times 22 = 4 \times 14$

$15 x + 12 - 88 = 56$

$15 x - 76 = 56$

$15 x = 132$

Divide both sides by $15$

$x = \frac{132}{15} \approx 8.8$

Jun 10, 2017

$x = \frac{44}{5}$

#### Explanation:

$\frac{1}{4} \left(5 x + 4\right) - \frac{22}{3} = \frac{14}{3}$

We can use the Distributive Property to simplify the left side:

$\frac{1}{4} \left(5 x\right) + \frac{1}{4} \left(4\right) - \frac{22}{3} = \frac{14}{3}$

We can now simplify the left side even further by multiplying the $\frac{1}{4}$ with the $5 x$ and canceling out the $4$'s in $\frac{1}{4}$ and $4$:

$\frac{5}{4} x + \frac{1}{\cancel{4}} ^ 1 \left({\cancel{4}}^{1}\right) - \frac{22}{3} = \frac{14}{3}$

Now, we can move all the constants over to the right side. Let's start by adding $\frac{22}{3}$ on both sides:

$\frac{5}{4} x + 1 = \frac{36}{3} = 12$

We now subtract $1$ on both sides:

$\frac{5}{4} x = 11$

And then we multiply both sides by $\frac{4}{5}$ to isolate $x$:

$x = \frac{11}{1} \cdot \frac{4}{5} = \frac{44}{5}$

.................................................................................................................................

Checking:

Being good mathematicians, we should always check our answers by substituting the value we got for the variable back into the locations of the variable in the original equation. Here, in this problem, we should substitute $x = \frac{44}{5}$ back into the original equation:

$\frac{1}{4} \left[5 \left(\frac{44}{5}\right) + 4\right] - \frac{22}{3} = \frac{14}{3}$

$\frac{1}{4} \left[{\cancel{5}}^{1} \left(\frac{44}{\cancel{5}} ^ 1\right) + 4\right] - \frac{22}{3} = \frac{14}{3}$

$\frac{1}{4} \left(48\right) - \frac{22}{3} = \frac{14}{3}$

$12 - \frac{22}{3} = \frac{14}{3}$

$12 = \frac{36}{3}$

$12 = 12$