# How do you solve 3.2(6x-7.2) = 0?

Apr 21, 2018

$x = 1.2$

#### Explanation:

1. Apply distributive property $a \left(b + c\right) = a \left(b\right) + a \left(c\right)$
$3.2 \left(\setminus \textcolor{c r i m s o n}{6 x} \setminus \textcolor{\mathmr{and} \chi d}{- 7.2}\right) = 0$ becomes...
$3.2 \left(\setminus \textcolor{c r i m s o n}{6 x}\right) + 3.2 \left(\setminus \textcolor{\mathmr{and} \chi d}{- 7.2}\right) = 0$
2. Simplify by multiplication
$\setminus \textcolor{c r i m s o n}{19.2 x} + \left(\setminus \textcolor{\mathmr{and} \chi d}{- 23.04}\right) = 0$
$19.2 x - 23.04 = 0$
3. Isolate the term with variable $x$ using addition
$19.2 x \setminus \cancel{- 23.04} \setminus \cancel{\textcolor{\to m a \to}{+ 23.04}} = 0 \setminus \textcolor{\to m a \to}{+ 23.04}$
$19.2 x = 23.04$
4. Isolate the variable $x$ by division
(\cancel(19.2)x)/(\cancel(\color(lightcoral)(19.2)))=23.04/(\color(lightcoral)(19.2)
$x = 1.2$
Apr 21, 2018

$x = \frac{18}{15} = 1.2$

In the absence of any instruction your solution format is the same as in the question.

#### Explanation:

Given: $\textcolor{g r e e n}{3.2 \left(6 x - 7.2\right) = 0}$

Divide both sides by $\textcolor{red}{3.2}$

$\textcolor{g r e e n}{3.2 \left(6 x - 7.2\right) = 0 \textcolor{w h i t e}{\text{dddd")->color(white)("dddd}} \underbrace{\frac{3.2}{\textcolor{red}{3.2}}} \left(6 x - 7.2\right) = \frac{0}{\textcolor{red}{3.2}}}$

color(green)(color(white)("dddddddddddddddddd")->color(white)("ddddd")1xx( 6x-7.2)=0

Add $\textcolor{red}{7.2}$ to both sides

color(green)(color(white)("dddd")6x-7.2=0color(white)("dddd") ->color(white)("ddddd")6xcolor(white)("d")ubrace(-7.2color(red)(+7.2)) = 0color(red)(+7.2)

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddddd") ->color(white)("ddddd")6xcolor(white)("d.d")+0color(white)("dddd}} = 7.2}$

Divide both sides by $\textcolor{red}{6}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddd")6x=7.2color(white)("ddddddd") ->color(white)("ddddd}} \frac{6}{\textcolor{red}{6}} x = \frac{7.2}{\textcolor{red}{6}}}$

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Determined that $x = \frac{7.2}{6}$ we find the decimal to be awkward. So we 'get rid of it!

$x = \frac{7.2 \times 10}{6 \times 10} = \frac{72}{60} = \frac{36}{30} = \frac{18}{15}$