|x|+2 is less than or equal to 13

Question

Absolute value

Answer 1

Note:  I am using [] to denote absolute values:

 

[x] + 2 ≤ 13

 

[x] ≤ 13-2

[x] ≤ 11

 

Absolute value is the distance a number is from zero, expressed as a positive number

For example:   [2] = 2    and   [-2] = 2

 

This means for [x] ≤ 11 then x must be greater than or equal to -11 and less than or equal to 11

because all numbers in that area will have an absolute value less than or equal to 11

 

-11 ≤ x ≤ 11

 

interval form:  [-11,11]

 

 

Answer 2

|x|+2 < 13             To solve absolute value problems, absolute value has to be all by itself. 

 

Therefore move over the 2 by subtracting it to the other side of equal sign.

 

|x|+2  -2  < 13  -2

 

|x| < 11    Now remove absolute value and  create 2 equations.  one with 11 and one with -11 & flip sign

 

x < 11  and x > -11    (Solution can also be graphed on number line where all the value from -11 &11 is shaded including both values)

 

 < _____________*****************____________________>

                               -11                0              11

 

 

 

Answer 3

We solve the inequality as if it were an equation.

 

| x | + 2 < 13

 

| x | < 11

 

 

We know that the absolute value of a negative number and a positive number give us a positive value.

 

x < 11               or             x > -11

 

 

This means the solution is all values of x greater than -11 and less than 11.

 

In interval notation

 

(-11 , 11)