The value |x−9|≤9 is equivalent to [18,0] in interval notation.
According to the statement
We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.
So, For find all x value we use absolute value inequalities.
distance of 9 from number 9.
So, when we draw the number line
we see that the number will become
The distance from x to 9 can be represented using an absolute value symbol, |x−9|.
Write the values of x that satisfy the condition as an absolute value inequality.
So, it become
|x−9|≤9
Now write two inequalities then it become
x−9≤9 and x−9≥−9
x≤18 and x≥0
So, The solution set is x≤18 and x≥0,
then the solution set is an interval including all real numbers between and including 18 and 0.
So |x−9|≤9 is equivalent to [18,0] in interval notation.
Learn more about absolute value inequalities here
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