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5 votes
|x-5| = 4x + 1
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1 Answer

4 votes

Answer: 4/5

Explanation:

Note that:


|x-5|=\begin{cases} x-5, x \geq 5 \\ 5-x, x < 5 \end{cases}

Case 1:
x \geq 5


x-5=4x+1\\\\-5=3x+1\\\\-4=3x\\\\x=-4/3

However, this does not fall within the required interval, so we disregard this solution.

Case 2:
x < 5


5-x=4x+1\\\\5=5x+1\\\\5x=4\\\\x=(4)/(5)

This solution falls within the required interval, so we include it in the solution set.

User Sharyn
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