(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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Piecewise Defined Function

**Physics Forums | Science Articles, Homework Help, Discussion**