Absolute value inequality help please?

Question

Okay, so I'm normally pretty good at math, but I have a test tomorrow and I got a few of these questions wrong on my homework today. So, I'm a little confused, and I need some help.

| 5x+2 | ≤ -2

I thought the answers were x is greater than or equal to 0 and x is less than or equal to -4/3, but my teacher said it was no solution. I don't understand. How is it no solution? And how do you no if the answer is no solution or all reals like the answer apparently is |4x-2| > -6?

Answer 1

First of all, do you go to AHS in mr. Tietell's class? 0.0! I think im in your class rofl.

Now, your teacher told you it is no solution because when you plug in the numbers, it probably doesn't work. Meaning the absolute value cannot equal to a negative number because absolute values are ALWAYS positive. If it does equal a negative number it is no solution. Just plug in the numbers you got in your answer, if the absolute value is positve and it equals a positive number, it works.

Btw, if you are in AHS, this is Jonah T =P!

Answer 2

|anything in here=positive number|

And any positive number is automatically larger than a negative number. So even if x=0, the problem would still be that 2 ≤ -2, which is obviously not right considering 2 is greater than -2. Since there is no possible number you can make x equal so that it would be true, there is no solution.

Answer 3

think about the numbers less than -2

when you take the absolute value of the expression, it is always positive

can a positive number ever be less than -2?

no solution would be the correct answer

next think about the number -6

when i place something in absolute values it always comes out positive

is a positive number always greater than -6?

the answer is yes, so your answer is all real numbers