l 2x+5 l < 6 solve for x values:

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l 2x + 5 l < 6

That means:

(2x+5) < 6 or -(2x+5) < 6

We could rewrite as follow:

==> -6 < 2x + 5 < 6

Subtract 5 from all sides:

==> -11 < 2x < 1

Now divide by 2:

==> -11/2 < x < 1/2

Then x values belong to the interval (-11/2, 1/2)

To solve |2x+5| <6

Solution:

When 2x+5 is positive , |2x+5| = 2x+5 <6 .

2x+5-5 < 6-5

2x< 1

2x/2 < 1/2

x<0.5........................(1).

When 2x+5 is -ve, |2x+5| <6 implies -(2x+ 5) < 6. Multiply by (-1) which reverses inequality.

2x+5 > -6

2x+5-5 > -6-5 =-11

2x >-11

2x/2 > -11/2 = -5.5................(2).

Combining (1) and (2), we get:

-5.5 < x < 0.5.

Or

x belongs to the open interval (-5.5 , 0.5)

To solve the inequality l 2x+5 l < 6, we'll apply the rule of the absolute values:

-6 < 2x+5 < 6

Now, we'll solve the left side of the double inequality:

-6 < 2x+5

We'll isolate 2x to the right side:

-6-5 < 2x

-11 < 2x

We'll divide by 2:

-11/2 < x

We'll solve the right side of the equation:

2x+5 < 6

We'll isolate to the left side, 2x:

2x < 6-5

2x < 1

We'll divide by 2 and since is not a negative value, the inequality remains the same:

x < 1/2

So, the interval of x values for the inequality to hold is:

**(-11/2 , 1/2)**

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