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if g(x) = 1/4x + 3/4 , determine x if g(x) = -3/2

Guest Jul 26, 2017
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 #1
avatar+1491 
+1

This is the given info:

\(g(x)=\frac{1}{4}x+\frac{3}{4}\)

\(g(x)=-\frac{3}{2}\)

 

\(g(x)=\frac{1}{4}x+\frac{3}{4}\) To solve for x, substitute -3/2 into the equation for g(x).
\(-\frac{3}{2}=\frac{1}{4}x+\frac{3}{4}\) I will simplify the right hand side of the equation.
\(-\frac{3}{2}=\frac{x}{4}+\frac{3}{4}\) Because x/4 and 3/4 have common denominators, I can add them together.
\(\frac{4}{1}*-\frac{3}{2}=\frac{x+3}{4}*\frac{4}{1}\) To get rid of the pesky fractions, multiply both sides of the equation by the lowest common multiple of all denominators present in the equation. Let's figure out what 4*-3/2 is.
\(\frac{4}{1}*-\frac{3}{2}=\frac{4*-3}{2*1}=\frac{-12}{2}=-6\) Insert this back into the original equation.
\(-6=x+3\) Subtract 3 on both sides.
\(-9=x\)  
   
TheXSquaredFactor  Jul 26, 2017
 #2
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+1

in step 4-5, when you were multiplying x+3/4 * 4/1, how is it changed to 4*-3/2*1? where did -3 and the denominator of 2 come from?

Guest Jul 27, 2017
 #3
avatar+1491 
0

Sorry, I did not respond sooner, but here is an explanation.

 

I also want to make sure that your question is clear. You want me to explain how to multiply \(\frac{4}{1}*-\frac{3}{2}\) in more detail, I think.

 

\(\frac{4}{1}*-\frac{3}{2}\) First, I am going to "tamper" with the -3/2.
\(-\frac{3}{2}\) There is a fraction rule that says that \(-\frac{a}{b}=\frac{-a}{b}\). In other words, I am moving the negative sign to the numerator, which is valid.
\(-\frac{3}{2}=\frac{-3}{2}\) Reinsert this into the original expression.
\(\frac{4}{1}*\frac{-3}{2}\) When multiplying fractions, you simply multiply the numerator and the denominator. In general, \(\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}\). I will apply this rule in the next step.
\(\frac{4*-3}{1*2}\) Now, evaluate the numerator and denominator separately.
\(4*-3=-12\hspace{1mm}\text{and}\hspace{1mm}1*2=2\) I have evaluated the numerator and denominator.
\(\frac{-12}{2}=-6\) Of course, with fractions, you should simplify them to simplest terms. This fractions ends up simplifying into an integer, -6. After this, I continue like normal.
   

 

Hopefully, this cleared up any confusion you had earlier. If it did not, reply with a burning question!

TheXSquaredFactor  Jul 29, 2017

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