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# input of -3/2?

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

Jul 26, 2017

#1
+2338
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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. $$-9=x$$
Jul 26, 2017
#2
+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
+2338
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