(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The equation [tex]\left| {x + a} \right| = \left| {x - b} \right|[/tex] has exactly one solution; at x=2. Find the value(s) of a and b

2. The attempt at a solution

Here is the way in which I have approached the situation:

[tex]

\begin{array}{l}

\left| {x + a} \right| = \left| {x - b} \right| \\

x + a = x + b \\

\end{array}

[/tex]

this solution is not possible as the x's on either side of the equation cancel each other out, and a is not equal to b, so;

[tex]

\begin{array}{l}

x + a = - x + b \\

2x + a = b \\

4 + a = b \\

a = k \\

a = k + 4 \\

\end{array}

[/tex]

However I'm not sure on my my final answer, as I have not evaluated the values for a or b, as i have left them in the term of k. However what I have interpreted from the question, I have not been given enough information. Thank you to those who reply, and correct me if anything I have stated is wrong

unique_pavadrin

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# Homework Help: Piecewise Defined Function

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