text: Homework Help: Piecewise Defined Function
  
  1. Mar 7, 2007
  
  1. The problem statement, all variables and given/known data
  The equation $$\left| {x + a} \right| = \left| {x - b} \right|$$ 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:
  $$\begin{array}{l} \left| {x + a} \right| = \left| {x - b} \right| \\ x + a = x + b \\ \end{array}$$
  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;
  $$\begin{array}{l} x + a = - x + b \\ 2x + a = b \\ 4 + a = b \\ a = k \\ a = k + 4 \\ \end{array}$$
  
  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
  
  2. Mar 7, 2007
  
  theperthvan
  
  Not sure how you got this step:
  $$\begin{array}{l} \left| {x + a} \right| = \left| {x - b} \right| \\ x + a = x + b \\ \end{array}$$
  If you are taking both to be positive, it should be $$x + a = x - b$$
  Then you can kill the x's. so a=-b.
  
  3. Mar 12, 2007
  
  ive used those steps as a simply does not equal -b as the x can be anywhere on the number line. by stating that a=-b, x is a fixed point at zero, which is incorrect as z is given the value of 2
  
  or is that completely wrong?
  thanks
explanation: The document is a homework help post about a piecewise defined function. It contains a math problem and an attempt at a solution, followed by a response from another user providing feedback. The post includes a question and an attempt at an answer, but the solution is not fully resolved.
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distilabel_metadata.content: Homework Help: Piecewise Defined Function
  
  1. Mar 7, 2007
  
  1. The problem statement, all variables and given/known data
  The equation $$\left| {x + a} \right| = \left| {x - b} \right|$$ 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:
  $$\begin{array}{l} \left| {x + a} \right| = \left| {x - b} \right| \\ x + a = x + b \\ \end{array}$$
  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;
  $$\begin{array}{l} x + a = - x + b \\ 2x + a = b \\ 4 + a = b \\ a = k \\ a = k + 4 \\ \end{array}$$
  
  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
  
  2. Mar 7, 2007
  
  theperthvan
  
  Not sure how you got this step:
  $$\begin{array}{l} \left| {x + a} \right| = \left| {x - b} \right| \\ x + a = x + b \\ \end{array}$$
  If you are taking both to be positive, it should be $$x + a = x - b$$
  Then you can kill the x's. so a=-b.
  
  3. Mar 12, 2007
  
  ive used those steps as a simply does not equal -b as the x can be anywhere on the number line. by stating that a=-b, x is a fixed point at zero, which is incorrect as z is given the value of 2
  
  or is that completely wrong?
  thanks
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a homework help post about a piecewise defined function. It contains a math problem and an attempt at a solution, followed by a response from another user providing feedback. The post includes a question and an attempt at an answer, but the solution is not fully resolved.
  
  Label: question-and-answer