Absolute values and solutions

Solve |x| = 5

{-5}
{5}
{-5, 5}(I picked this,but im unsure if its right)

Solve 2|x| = 3

{-3/2, 3/2}

I really need help with the second one though

Question

Absolute values and solutions

Solve |x| = 5


{-5}
{5}
{-5, 5}(I picked this,but im unsure if its right)


Solve 2|x| = 3


{-3/2, 3/2}

I really need help with the second one though

hero · Answer

In general, 

$$|a| = \pm a$$

anonymous · Answer

Can you elaborate more

hero · Answer

Well, if you're trying to solve for x in this manner, then to solve

|x| = 5 you write: $x = \pm 5$

The $\pm$ means 'plus or minus'

Absolute value is another way of saying 'distance from zero' on a number line. 

So is someone says |5| is 5, what they are really saying is the distance from 0 to 5 is the same as the distance from 0 to -5, and that distance is 5 units.

anonymous · Answer

Thanks for that do you know anything about the second one?

hero · Answer

You isolate the |x| to get

$$|x| = \frac{2}{3}$$

Then from there, you use the same reasoning from the previous problem to arrive at the correct result.