can someone help me solve a simple math problem?

Question

absolute value inequality

let me use " / " for the absolute value symbol

-2/4x + 3/ < -4

if you could help and explain a little on how you did it, that would be greatly appreciated.
Thank you

Answer 1

First off, think of 4x + 3 as u.

-2u < -4
u > 2
(when you divide both sides the sign in the middle changes)

Because it's the absolute value, 4x + 3 > 2, or 4x + 3 < -2

4x + 3 > 2
4x > -1
x < -0.25

4x + 3 < -2
4x < -5
x > -1.25

Therefore -1.25 < x < -0.25

Answer 2

First we must divide by –2 and isolate the absolute value symbols and what is in them, thus obtaining

/4x + 3/ < 2.

Since /4x + 3/ < 2, we can remove the absolute value symbols and obtain

–2 < 4x + 3 < 2.

Now we must subtract 3 from all three parts of the equation to obtain

–5 < 4x < –1.

To isolate x, we must divide all three parts of the equation by 4 to obtain

–1.25 < x < –0.25.

Answer 3

divide so that it is /4x+3/>2, then go 4x+3<-2, which gives you x<-5/4, and 4x+3>2, which is x>-1/4. so it would be -1/4>x>-5/4

Answer 4

x> -1/4 or x< -5/4

Answer 5

|4x + 3| > 2
4x + 3 > 2 or 4x+3 < -2
4x > -1 or 4x < -5
x < -1/4 or x < -5/4

Answer 6

i'm unsure what precisely you're asking. in case you need to simplify the 1st equation, you're able to try this via factoring out the 8, wherein case you get 8*(2x - a million) this is basically a distinctive form of the unique given equations. For the 2nd you may ought to multiply it out, so which you have (3x-2y)(3x-2y) = 9x^2 - 6xy - 6xy + 4y^2 = 9x^2 - 12xy + 4y^2. desire this helps, yet whilst not, you need to offer extra information with reference to the concern.