solve for x if l 2x -3 l < 5
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l 2x - 3 l < 5
Let us rewrite:
==> (2x -3 ) < 5 OR -(2x -3) < 5
Or we could write:
-5 < 2x - 3 < 5
Now add 3 to all sides:
==> -2 < 2x < 8
Now divide by 2:
==> -1 < x < 4
Then x belongs to (-1, 4)
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The inequality l 2x -3 l < 5 has to be solved for x.
The absolute value of a number |x| is equal to x if x>=0 and it is equal to -x if x <0
|2x - 3| < 5
Assume 2x - 3 >=0 or 2x >= 3 or x >= 3/2
2x - 3 < 5
2x < 8
x < 4
The permissible values of x are [3/2, 4)
Assume 2x - 3 < 0 or x < 3/2
3 - 2x < 5
-2x < 2
x > -1
The permissible values of x are (-1, 3/2)
Combining the two solution sets the values that x can take lie in (-1, 4)
To solve the inequality l 2x -3 l < 5, we'll apply the rule of the absolute values:
-5 < 2x-3 < 5
Now, we'll solve the left side of the double inequality:
-5 < 2x-3
We'll isolate 2x to the right side:
-5+3 < 2x
-2 < 2x
We'll divide by 2:
-2/2 < x
-1 < x
We'll solve the right side of the equation:
2x-3 < 5
We'll isolate to the left side, 2x:
2x < 5+3
2x < 8
We'll divide by 2 and since is not a negative value, the inequality remains the same:
x < 4
So, the interval of x values for the inequality to hold is:
(-1 , 4)
To solve |2x-3| < 5
Solution:
WHen 2x-3 > 0, |2x-3| < 5 implies, 2x-3 < 5,
2x-3 < 5,
2x < 5+3,
2x/2 < 8/2,
x < 4.................(1)
When 2x-3 < 0, |2x-3| < 5 implies 3-2x <5
3-5 < 2x,
-2 < 2x,
-2/2 < 2x/2,
-1 < x.................(2).
Combining the two inequalities at (1) and (2), we get:
-1 <x < 4.
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