# How do you solve .02( x - 100) + .06x = 62?

Sep 16, 2017

$x = 80$

#### Explanation:

The first thing to do is to multiply the terms in the bracket. To do this, consider the rule that $a \left(b + c\right) = a b + a c$, and apply this rule to the terms we have here, $0.2 \left(x - 100\right)$, where $0.2 = a$, $x = b$ and $- 100 = c$ After multiplying, the equation now looks like
$0.2 x - 2 + 0.6 x = 62$
Next we group all like terms together. As you can see, there are 2 terms of $x$, $0.2 x$ and $0.6 x$. Simply add these two terms together to get
$0.8 x - 2 = 62$

The third step is to isolate the $x$-term, and to do this we add the opposite value of $- 2$ to both sides of the equation, which happens to be $2$. The equation now looks like this:
$0.8 x = 64$
The last step to do is divide both sides by $0.8$. Notice how the $x$-term $0.8 x$ is equal to $0.8 \cdot x$. Since we want to isolate $x$, we use the reverse operator on the coefficent of $x$. The coeffiecent is 0.8, and the reverse operator is division, therefor we divide both sides of the equation by 0.8 to get
$x = 80$

To prove this, substitute $x$ for 80 in the original equation.

I hope that helped!