Question

1. for which value of ( k ) does the equation ( |x + 14| + 5 = k ) have one real solution?

Explanation:

Step1: Isolate the absolute value

Rearrange the equation to isolate the absolute value term.
$|x+14| = k - 5$

Step2: Analyze absolute value properties

An absolute value expression $|A| = c$ has exactly one real solution if and only if $c=0$, since absolute value is non-negative, and only 0 maps to a single input.
$k - 5 = 0$

Step3: Solve for k

Solve the linear equation for k.
$k = 5$

Answer:

$k=5$