GCF and LCM what is it and what do i have to do

1 answer:

kondor19780726 [428]3 years ago

6 0

GCF is the Greatest Common Factor. It would be the largest number that can divide evenly into all the numbers you need to find the GCF in.

exapmple GCF for 12 and 16

12: 1, 2, 3, 4, 6, 12

16: 1, 2, 4, 8, 16

the largest common number is 4, so 4 is the GCF of 12 & 16

LCM = Least Common Multiple is the smallest number ( other than zero) that is a multiple of both

LCM of 3 and 5

3: 3, 6, 9, 12, 15, 18
5: 5, 10, 15, 20
the first common number is 15, so this is the LCM of 3 & 5

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$\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}$

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$\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}$

$\underline{\boldsymbol{\sf{Answer}}}$

$\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }$

$\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}$