|4x| > 8 AND how do I solve and GRAPH this!?

Answer 1

|4x| > 8

Use the property |ab| = |a| |b|

|4| |x| > 8

And |4| = 4, so

4|x| > 8

Divide both sides by 4,

|x| > 2

And any inequality of the form |z| > c translates to
[ z > c ] OR [ z < -c ], so

[ x > 2 ] OR [ x < -2 ]

The solution set:

{x | x > 2 OR x < -2, for all real numbers x}

In interval notation:

(-infinity, -2) U (2, infinity)

This is graphed on a number line as opposed to an x-y graph.

On a number line, open circle at -2, thick arrow leftward.
Open circle at 2, thick arrow rightward.

Answer 2

By definition:
If 4x>=0 <=> x>=0 then
|4x| = 4x > 8 <=> x>2
If 4x<0 <=> x<0 then
|4x| = -4x > 8 <=> x<-2
The results: x>2 or x<-2
BY GRAPH
1. Draw graph of 4x this is one line passing (0,0) and (1,4)
2. Reflect a branch (which under X-axis) in X-axis we have graph of |4x|. This graph is two rays (semilines) from (0,0), one passing (1,4), other passing (-1,4)
3. Draw a line y = 8. This is a line passing (0,8) and parallel with X-axis.
4. Take all x such that graph of |4x| is higher (over) than graph of 8. The results are the same x<-2 or x>2

Answer 3

First, you need to solve it:
4x > 8
x > 2

4x > -8
x < -2

x > 2 OR < -2

So to graph, you would draw a number line with an open circle on 2 and an open circle on -2. Shade everything greater than 2 and less than -2 (so the only thing not shaded is the region between 2 and -2)

Answer 4

The absolute value of 4x > 8 means all x>2 and x<-2.

A graphical representation of this relationship is the area of the x,y plot where y > 8 and x > +2 and x < -2.

Answer 5

4X+4>3X+8 Take the selection related to the variable it relatively is the smallest and pass from there you spot that 3X is smaller than 4X so which you subtract the 3X from the 4X What do you do there? So now X+4>8 (Now undergo in techniques in case you ever / a - selection you turn the > to < undergo in techniques that rule!!) So now you have that and now in basic terms - 4 and sparkling up!

Answer 6

There are two possibilities for absolute value:
4x>8
x>2

-(4x)>8
x<-2

<===()---------()===>
........-2...........2

Written as x>2 or x<-2. Graph with open circles. The = sign indicates what needs to be darkened.