Question

Write the expression |x − 3| + |x − 9| without the absolute value symbols if x is in the given interval.[3, 9]

Answer 1

`f(x)=x-3-(x-9)`

1) The way to evaluate that Absolute Value expression is to remove the absolute value bars this way, considering this to be a function

Consider x is between [3,9]

`\begin{gathered} ---- \\ 3\leq x\leq9 \\ f(x)=x-3+-(x-9) \\ f(x)=x-3-x+9 \\ f(x)=6 \end{gathered}`

Then we can rewrite that absolute value function, considering that all whole values for the first absolute bar will be 0 or positive, and at the same time all the values will be lesser than 9 or equal to zero.

2) Thus the answer is:

`f(x)=x-3+-(x-9)`