Please help Simplify to an answer in the form of ax + b for x in [3,5]. $\displaystyle |x-2| - 4 |x-6| $
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For all $\displaystyle x \in [3, 5], x - 2$ is positive and $\displaystyle x - 6$ is negative. Thus, for all $\displaystyle x \in [3, 5], |x - 2| = x - 2$ and $\displaystyle |x - 6| = 6 - x$.
Originally Posted by BadMaterial Please help Simplify to an answer in the form of ax + b for x in [3,5]. $\displaystyle |x-2| - 4 |x-6| $ |x-2| = (x-2) because (x-2)>0 for $\displaystyle x\in[3,5]$. |x-6| = -(x-6) because (x-6)<0 for $\displaystyle x\in[3,5]$. Use these properties: $\displaystyle |x-2| - 4 |x-6| = (x-2)-4(-(x-6))$ I'll leave the rest for you.
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