Question
\( -5=-|c-5|+3 \) he solution set is \( \square \)
Ask by Carrillo Donnelly. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is { -3, 13 }.
Solution
We start with the equation:
-5 = -|c - 5| + 3
Step 1. Isolate the absolute value term by subtracting 3 from both sides:
-5 - 3 = -|c - 5|
-8 = -|c - 5|
Step 2. Multiply both sides by -1:
8 = |c - 5|
Step 3. Solve the absolute value equation:
|c - 5| = 8 implies c - 5 = 8 or c - 5 = -8
Solving each case:
For c - 5 = 8:
c = 8 + 5 = 13
For c - 5 = -8:
c = -8 + 5 = -3
Thus, the solution set is { -3, 13 }.
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Simplify this solution Beyond the Answer
To solve the equation \( -5 = -|c-5| + 3 \), we first isolate the absolute value term: \[ -5 - 3 = -|c-5| \] \[ -8 = -|c-5| \] Now, multiplying through by -1 gives: \[ |c-5| = 8 \] This absolute value equation means \(c-5\) can equal 8 or -8, so we can set up two equations: 1. \( c - 5 = 8 \) leads to \( c = 13 \). 2. \( c - 5 = -8 \) leads to \( c = -3 \). Thus, the solution set is \(\{ -3, 13 \}\).
