# How do you solve 5.3 + u = 3.2u -2.7?

Jun 4, 2016

color(blue)(u = 3.64

#### Explanation:

5.3 + u = 3.2 u − 2.7

5.3 + color(blue)(u) = color(blue)(3.2 u) − 2.7

5.3 + 2.7 = color(blue)(3.2 u − u )

$8 = 2.2 u$

$u = \frac{8}{2.2}$

color(blue)(u = 3.64 rounded to the nearest $100$

Jun 4, 2016

Same thing with a touch more explanation

$u = 3 \frac{11}{23} \text{ this is an exact answer!}$

#### Explanation:

Given:$\text{ } \textcolor{b r o w n}{5.3 + u = 3.2 u - 2.7}$

Subtract $\textcolor{b l u e}{u}$ from both sides

$\text{ } \textcolor{b r o w n}{5.3 + u \textcolor{b l u e}{- u} = 3.2 u - 2.7 \textcolor{b l u e}{- u}}$

But $u - u = 0$

$\text{ } 5.3 + 0 = 3.2 u - u - 2.7$

But $3.2 u - u = 2.3 u$

$\text{ } 5.3 = 2.3 u - 2.7$

Add $\textcolor{b l u e}{2.7}$ to both sides

" "color(brown)(5.3color(blue)(+2.7)=2.3u-2.7color(blue)(+2.7)

But $5.3 + 2.7 = 8.0 \text{ and } - 2.7 + 2.7 = 0$

$\text{ } 8 = 2.3 u + 0$

Divide both sides by 2.3

$\text{ } \frac{8}{2.3} = \frac{2.3}{2.3} \times u$

But $\frac{2.3}{2.3} = 1 \text{ so } u = \frac{8}{2.3}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

But dividing $2.3 \text{ into } 8$ gives a never ending decimal so the answer would not be accurate. It is much more accurate to express it as a fraction.

So write $\text{ "u=8/2.3" }$ as $\text{ } u = \frac{8 \times 10}{2.3 \times 10} = \frac{80}{23}$

$\implies u = 3 \frac{11}{23}$