Question

question
solve for all values of a in simplest form.
19 = |10 - a|
answer attempt 1 out of 2
+ additional solution - no solution
a =
submit answer
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Explanation:

Step1: Recall absolute value definition

The equation \(|x| = k\) (where \(k\geq0\)) implies \(x = k\) or \(x=-k\). So for \(19 = |10 - a|\), we have two cases:
Case 1: \(10 - a=19\)
Case 2: \(10 - a=- 19\)

Step2: Solve Case 1

Solve \(10 - a = 19\) for \(a\).
Subtract 10 from both sides: \(-a=19 - 10\)
\(-a = 9\)
Multiply both sides by - 1: \(a=-9\)

Step3: Solve Case 2

Solve \(10 - a=-19\) for \(a\).
Subtract 10 from both sides: \(-a=-19 - 10\)
\(-a=-29\)
Multiply both sides by - 1: \(a = 29\)

Answer:

\(a=-9\) or \(a = 29\)