# How do you solve 4.7(2f - 0.5) = -6(1.6f - 8.3f)?

Sep 28, 2015

$f = - \frac{47}{616}$

#### Explanation:

We first start out by using the distributive property; that's $a \left(b + c\right) = a b + a c$. Let me demonstrate:

$4.7 \left(2 f - 0.5\right) = - 6 \left(1.6 f - 8.3 f\right)$ (original problem)
$\left(4.7 \cdot 2 f - 4.7 \cdot 0.5\right) = - 6 \left(1.6 f - 8.3 f\right)$ (distributing the 4.7)
$9.4 f - 2.35 = - 6 \left(1.6 f - 8.3 f\right)$ (simplifying)

Now to combining like terms and a little multiplying:

$9.4 f - 2.35 = - 6 \left(- 6.7 f\right)$ (combining the $1.6 f$ and $- 8.3 f$)
$9.4 f - 2.35 = 40.2 f$ (multiplying the $- 6$ and $- 6.7 f$)

Now we proceed to solving this 2-step equation:

$- 2.35 = 30.8 f$ (subtracting $9.4 f$ from both sides)
Here, we encounter a problem: to finish, we need to divide by $30.8$; that way, we solve for $f$. But in doing so, we get a repeating decimal. This would be nice for an approximate answer, but we want something definite. So, we convert our decimal numbers to whole numbers by multiplying by 100. Watch:

$- 2.35 \cdot 100 = 30.8 f \cdot 100$
$- 235 = 3 , 080 f$

It certainly isn't pretty, but it works. Finally, finally, we divide by $3 , 080$ to get our result:

$f = - \frac{235}{3 , 080}$
$f = - \frac{47}{616}$ (simplifying the fraction)

Hey, it's a weird answer, but the math never lies. Our result is $f = - \frac{47}{616}$.

Sep 28, 2015

First collect like terms inside the brackets;
#4.7(2f-0.5)=-6(-6.7f)

Then, you would want to multiply into the brackets;
$9.4 f - 2.35 = 40.2 f$

Collect like terms on either side of the equals sign;

$- 2.35 = 30.8 f$

Divide both sides by 30.8;

$- \frac{2.35}{30.8} = \frac{30.8 f}{30.8}$

Finally, compute the result;

$f = - \frac{47}{616}$

Hope that helps :)