# 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)

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.