# Question 88ca9

Oct 20, 2017

$c = 3$

#### Explanation:

$0.2 \left(10 - 5 c\right) = 5 c - 16$

In order to solve this, we need to isolate $c$, which means get it by itself. So, let's start by getting rid of those parentheses and distributing that $0.2$.

$0.2 \left(10 - 5 c\right) = 5 c - 16$

$2 - 1 \cdot c = 5 c - 16$

Now let's get all the $\textcolor{\mathmr{and} a n \ge}{c o n s t a n t s}$ (numbers) on one side

subtract 2 on both sides

$- c = 5 c \textcolor{\mathmr{and} a n \ge}{- 16 - 2}$

Now let's get the color(blue)(variab l es_# on one side

subtract $5 c$ from both sides

$\textcolor{b l u e}{- c - 5 c} = - 16 - 2$

Let's combine everything and see what we've got

$- 6 c = - 18$

We're almost there, but $c$ still isn't by itself. We need to get rid of that pesky $- 6$

divide by $- 6$ on both sides

$c = \frac{- 18}{-} 6$

$c = 3$
$. . . . . . . . . . . . . . . . . . . . . . . .$

To check our work, let's plug in $3$ for $c$ and make sure both sides are equal:

$0.2 \left(10 - 5 \textcolor{red}{c}\right) = 5 \textcolor{red}{c} - 16$

$0.2 \left(10 - \left(5 \cdot 3\right)\right) = \left(5 \cdot 3\right) - 16$

$0.2 \left(10 - 15\right) = 15 - 16$

$0.2 \left(- 5\right) = - 1$

$\textcolor{g r e e n}{- 1 = - 1}$

We were right! Great job