Question

How do you solve x6≤−2?

Answer 1

Answer:

Step-by-step explanation:

The absolute value of x is written as \displaystyle |x|∣x∣. It has the following properties:

If  

x

≥

0

,

then  

|

x

|

=

x

.

If  

x

<

0

,

then  

|

x

|

=

−

x

.

For real numbers \displaystyle AA and \displaystyle BB, an equation of the form \displaystyle |A|=B∣A∣=B, with \displaystyle B\ge 0B≥0, will have solutions when \displaystyle A=BA=B or \displaystyle A=-BA=−B. If \displaystyle B<0B<0, the equation \displaystyle |A|=B∣A∣=B has no solution.

An absolute value equation in the form \displaystyle |ax+b|=c∣ax+b∣=c has the following properties:

If  

c

<

0

,

|

a

x

+

b

|

=

c

has no solution

.

If  

c

=

0

,

|

a

x

+

b

|

=

c

has one solution

.

If  

c

>

0

,

|

a

x

+

b

|

=

c

has two solutions

.