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

The (absolute value) x-20 (absolute value) is less than or equal to 6. I did it first with six positive and got x is lesss than or equal to 26. Then I made the six negative and got x is less than or equal to 14. But this is impossible for these to both be true, right? How come my book says no solution isn't an answer? (It has 14 is less than or equal to x which is less than or equal to 26 as the answer). How did they get this?

- Algebra -
**bobpursley**, Monday, October 12, 2009 at 4:57pm
abs(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 4:59pm
The 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]

## Answer this Question

## Related Questions

- calculus - Let M=1000. Which of the conditions is equivalent to f(x)= 1/((4x-12...
- math !!!!!!please part of a major grade!!!!!! - when in the absolute value of x ...
- calculus - Consider the function f(x)=(x^3)(e^9x), -2 is less than or equal to x...
- math - when in the absolute value of x equal to the absolute value of negative x...
- math, help - For the following set, which number has the largest absolute value...
- Calculus - Consider the function f(x) = x^4 - 72 x^2 + 3, -5 less than or equal...
- Math - 1. Suppose a and b are integers, and the absolute value of a is > than...
- Algebra - In my algebra b ook it says if a is less than 0, the absolute value of...
- algerbra 2 please! this is part of a major grade!! - How do I solve this: The ...
- math, calculus - Use the MVT to prove: absolute value of (sin(a)-sin(b)) is less...

More Related Questions