The answer is that -4.5 < x < 1.5. Here is how to find this answer.

What we are saying is that

(2x +3) < 6 and that 6 > -(2x-3)

That is because we are looking for the absolute value of the expression.

Another way to say this is that

-6 < 2x + 3 < 6

So first we have to subtract 3 from all sides. That gives us

-9 < 2x < 3

So then we have to divide all sides by 2. That gives us

-4.5 < x < 1.5

I am assuming that you need to solve for x?

l 2x + 3 l < 6

That means:

(2x+3) < 6

-(2x+3) < 6 ==> 2x + 3 > -6

==> -6 < 2x+3 < 6

subtract 3 from all sides:

==> -9 < 2x < 3

Now divide all sides by 2

==> -4.5 < x < 1.5

Then x belongs to the interval (-4.5, 1.5)

-6<2x+3<6

We'll solve first:

-6<2x+3

We'll add 6 both sides:

0<2x+3+6

0<2x+9

We'll subtract 9 both sides:

-9<2x

We'll divide by 2 both sides:

-4.5<x

Now, we'll solve:

2x+3<6

We'll subtract 3 both sides, in order to isolate x:

2x<6-3

2x<3

We'll divide by 2 both sides:

x<1.5

So, the range of values of x is:

**-4.5<x<1.5**

To solve |2x+3|< 6.

solution:

|2x+3| < 6 maens :

When 2x+3 >0 2x+3 < 6 or when 2x+3 < 0, 2x+3 > -6.

When 2x+3 > 0,

2x+3 > 6

2x > 6-3 = 3

x > 3/2 = 1.5............(1)

When 2x+3 < 0,

2x+3 > -6

2x > -6-3 = -9

x > 9/2 = -4.5. Or -4.5 < x............(2)

Combining Both cases, -4.5 < x < 1.5

solving for x

12x+31<6

1. 12x<-25

2. x< -25/12=-2.0833 (do this problem so as not to have a rounding error)

3. x = -2.0833...

but doing this problem to check i think you have it set up wrong because i got 6 when it should be less than so im not sure...i did it right, use your calculator the whole time so you dont have a rounding error..hope this helped...

punch this into your claculator..

6 minus 31 equals(do not clear) divide by 12 equals (do not clear) but this answer is what x equals...then check it by multipling the answer by 12 and adding 31, this answer should be less than 6 but when i did it i got 6 so maybe your question is incorect, is the less than sign supposed to have a line under it meaning less than or equal to six if so than that is the right answer of -2.0833...

solving for x

12x+31<6

1. 12x<-25

2. x< -25/12=-2.0833 (do this problem so as not to have a rounding error)

3. x = -2.083