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August 28, 2014

August 28, 2014

Posted by **Andrea** on Monday, October 12, 2009 at 4:47pm.

- Algebra -
**bobpursley**, Monday, October 12, 2009 at 4:57pmabs(x-20)<=6

but absolute anything is greater than zero, so

0<=abs(x-20)<=6

which now means x can go to 14 to 26, right?

Now, why in the world did you solve it for

abs(x-20)>=-6 If that had be the question, you would be right, however, it is not the problem.

- Algebra -
**MathMate**, Monday, October 12, 2009 at 4:59pmThe answer is not a single number, because it is an inequality. Inequalities in the real domain (ℝ) has infinite number of solutions, and is expressed in the form of an interval.

When dealing with the absolute value function, it makes life easier to split the inequality into two equations. After that, the two solution sets will be intersected to give the final solution.

For example, to solve

|x-3| ≤ 2

we write

x-3 ≤ 2 ....(1), and

-(x-3) ≤2 ....(2).

The solution of (1) gives

x≤5

and the solution of (2) gives

x≥1

So the answer would be

1≤x≤5, or expressin interval notation,

x ∈ [1,5]

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