# How do you solve 1/4t + 5 = 3/4t - 2?

Jul 15, 2015

I found: $t = 14$

#### Explanation:

You can collect terms with $t$ on the left and get:
$\frac{1}{4} t - \frac{3}{4} t = - 2 - 5$
$\frac{1 - 3}{4} t = - 7$
$- \frac{2}{4} t = - 7$
$- \frac{1}{2} t = - 7$
rearranging:
$t = 14$

Jul 15, 2015

I would solve it by multiplying all terms (on both sides) by $4$ and then perform the normal arithmetic operations to get $t = 14$.
(other people might like working with the fractions).

#### Explanation:

Given $\frac{1}{4} t + 5 = \frac{3}{4} t - 2$

If we multiply all terms by $4$ to get rid of the fractions:
$\textcolor{w h i t e}{\text{XXXX}}$$t + 20 = 3 t - 8$

We can add $\left(8 - t\right)$ to both sides
$\textcolor{w h i t e}{\text{XXXX}}$$28 = 2 t$

Flipping the equation ('cause I like it better that way) and dividing by 2
$\textcolor{w h i t e}{\text{XXXX}}$$t = 14$