Question

|x+18|=1

Answer 1

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:
Answer:  x = -17 or x = -19

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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:

Answer:  x = -17 or x = -19

Answer 2

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:

$|x|= \left \{ {{x, \ \ \ x \ \geq \ 0} \atop {-x, \ \ \ x \ \ \textless \ \ 0}} \right.$

Thus, for $|x+18|=1$, we split the absolute value as such:

$x+18=1$ and $x+18=-1$

We solve each case.

$x=-17$ and $x=-19$

We check these solutions.

$|-17+18|=1\\|1|=1\\1=1$
and
$|-19+18|=1\\|-1|=1\\1=1$