|x+18|=1 everyone, only one attempt to ! 40pointsthe lines are absolute value

The absolute value, or modulus, of a number is its distance from zero, or essentially its magnitude.

The absolute value produces a positive answer.

We have this definition for the absolute value, taking into account its different values for different signs:



Thus, for , we split the absolute value as such:

and 

We solve each case.

and 

We check these solutions.


and

Solve for x over the real numbers:
abs(x + 18) = 1

Split the equation into two possible cases:
x + 18 = 1 or x + 18 = -1

Subtract 18 from both sides:
x = -17 or x + 18 = -1

Subtract 18 from both sides:
  x = -17 or x = -19



Solve for x over the integers:
abs(x + 18) = 1

Split the equation into two possible cases:
x + 18 = 1 or x + 18 = -1

Subtract 18 from both sides:
x = -17 or x + 18 = -1

Subtract 18 from both sides:

  x = -17 or x = -19