Solve |2x + 1| < 3 or |2x +1| > 3.
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calendarEducator since 2008
write3,662 answers
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Given the inequality:
l 2x +1 l < 3
By definition, we can rewrite:
-3 < 2x+1 < 3
Now we will subtract -1 from all sides.
==> -4 < 2x < 2
Now we will divide by 2.
==> -2 < x < 1
Then the values of x belongs to the interval (-2, 1)
.....l......l......l___l__l___l......l......l......l.......
-4 -3 -2 -1 0 1 2 3 4
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calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
To draw the graph of |2x + 1| >3, remember that
|2x +1| = 2x + 1 , when 2x + 1 > 0
and -(2x + 1) when 2x + 1 < 0
So we have two inequations here.
2x + 1 > 3, for 2x + 1> 0
=> 2x > 2 and 2x > -1
x > 1 satisfies both
-(2x + 1) > 3 for 2x + 1 < 0
=> 2x + 1 < 3
=> 2x < 2 and x < -1/2
=> x < -1/2 satisfies both.
So the required graph would have all values of x with x > 1 and x < -1/2