Question 312490: How would you solve following inequality?
|2x-3|>5 Found 3 solutions by rapaljer, Fombitz, Edwin McCravy:Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website! First, I would recognize that since this is an ABSOLUTE VALUE problem that ais GREATER THAN a positive number, this is an EXTREMES problem. It has two categories of solutions:
First solutions:
2x-3 > 5
2x >8
x>4
Second solutions:
2x-3 < -5
2x <-2
x<-1
In interval notation, this would be (-inf, -1) U (4, inf).
You can put this solution on YOUR website! Two solutions: and
Positive solution:
.
.
.
Negative solution:
The solution set is (,)U(,).
.
.
.
Verified graphically,
|2x - 3| > 5
That says 2x - 3 is either less than -5 or else it's greater than +5,
but not inclusive of either -10 or +10 since the symbol
of inequality is > and not >
And that is the same thing as saying:
2x - 3 < -5 OR 2x - 3 > +5
Add 3 to both sides in both inequalities to get 2x alone
on the left of each one
2x - 3 < -5 OR 2x - 3 > +5
+ 3 +3 + 3 +3
---------------------------
2x < -2 OR 2x > 8
Divide both sides of both inequalities by 2 to solve for x
in each one:
< OR < >
x < -1 OR x > 4
on a number line that has this graph:
<========================o-------------------o====================>
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
In interval notation, that's (, -1) U (4, )
Edwin
