Question

solve for all values of x in simplest form. 46 = |x + 27|

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|A| = B\) (where \(B\geq0\)) implies \(A = B\) or \(A=-B\). Here, \(A = x + 27\) and \(B = 46\) (and \(46\geq0\)), so we have two cases:
Case 1: \(x + 27 = 46\)
Case 2: \(x + 27=-46\)

Step2: Solve Case 1

Subtract 27 from both sides of \(x + 27 = 46\):
\(x=46 - 27\)
\(x = 19\)

Step3: Solve Case 2

Subtract 27 from both sides of \(x + 27=-46\):
\(x=-46 - 27\)
\(x=-73\)

Answer:

\(x = 19\) or \(x=-73\)