#1**+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**+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**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