Solve the inequality, and express the solutions in terms of intervals whenever possible.
2<|x-6|<4

Question

Solve the inequality, and express the solutions in terms of intervals whenever possible.  2&amp;lt;|x-6|&amp;lt;4

sukljama2 · Accepted Answer

Step 1
We have to solve the inequality for x . we can use two methods to solve this inequality . in the first method we can solve the inequality using absolute value formulas.
if $| x | \leq r t h e n - r \leq x \leq r$
if we have $| x | \geq r$ , we can write it as $| x | \leq - r$ and we can use the above form .
here we have x-6 in the place of x.
Step 2
Consider the inequality 2<|x-6|<4, we have to solve this inequality for the values of x by using the formula
$| x | \leq r$ , we get $- r \leq x \leq r$ and if $| x | \geq r$ we can write it as $| x | \leq - r$ .
Now consider the first part of the inequality
2<|x-6|
|x-6|>2
|x-6|<-2
now we can use the form $- r \leq x \leq r$
-(-2)<(x-6)<-2
2 6+2 8 Now take the second part of the inequality
|x-6|<4, which can be simplified using the form $- r \leq x \leq r$
-4 -4+6 2 Now combining two inequalities 8 we get
2 Hence we have the interval form for the above inequality is $(2, 4) \cup (8, 10)$ .

Solve the inequality, and express the solutions in terms of

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