Question

HELP I NEED AN EXPLANATION IM CONFUSED |3x|>-12 is x>−4 or x<4 but I dont know how that is. I thought it was no solution.. can someone explain.

Answer 1

see below (I hope this helps!)

Explanation:

|3x| > -12

There are two cases, x is either positive (in which |3x| = 3x) or negative (in which |3x| = -3x). Therefore:

3x > -12 or -3x > -12

x > -4 or x < 4 (Remember, multiplying / dividing an inequality by a negative number flips the sign.)

Answer 2

All real numbers.

Explanation:

So we have the equation:

`|3x|>-12`

Remove the absolute value bars. Definition of absolute value:

`3x>(-12)\text{ or } 3x<-(-12)`

Note that we change the sign on the right because we multiplied by a negative.

Divide both sides by 3:

`x>-4\text{ or }x<4`

Now, look at this inequality. This says that the solution is all the numbers to the right of -4 and all numbers to the left of 4.

I've provided a number line. The red line represents x>-4 and the blue line represents x<4.

As you can see, every value is covered both towards the left and the right.

In other words, our answer is all real numbers.