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

2 Answers
Sep 28, 2015

Answer:

#f = -47/(616)#

Explanation:

We first start out by using the distributive property; that's #a(b+c) = ab+ac#. Let me demonstrate:

#4.7(2f-0.5) = -6(1.6f-8.3f)# (original problem)
#(4.7*2f-4.7*0.5) = -6(1.6f-8.3f)# (distributing the 4.7)
#9.4f-2.35 = -6(1.6f-8.3f)# (simplifying)

Now to combining like terms and a little multiplying:

#9.4f-2.35 = -6(-6.7f)# (combining the #1.6f# and #-8.3f#)
#9.4f-2.35 = 40.2f# (multiplying the #-6# and #-6.7f#)

Now we proceed to solving this 2-step equation:

#-2.35 = 30.8f# (subtracting #9.4f# 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*100 = 30.8f*100#
#-235 = 3,080f#

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

#f = -235/(3,080)#
#f = -47/(616)# (simplifying the fraction)

Hey, it's a weird answer, but the math never lies. Our result is #f = -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;
#9.4f-2.35=40.2f#

Collect like terms on either side of the equals sign;

#-2.35=30.8f#

Divide both sides by 30.8;

#-2.35/30.8=(30.8f)/30.8#

Finally, compute the result;

#f=-47/616#

Hope that helps :)