Given that $a>0$ and $b<0$, which of the following expressions is equivalent to $|a|−|b|$ for any values of a and b?

To determine which expression is equivalent to $|a| - |b|$ given that $a > 0$ and $b < 0$, let's analyze the situation step by step.

1. Absolute Values

• Since $a > 0$, $|a| = a$.



• Since $b < 0$, $|b| = -b$.

2. Expression to Evaluate

$<br><br> |a| - |b| = a - (-b) = a + b<br><br>$

3. Analyzing the Options

• 
  
  a) $|a - b|$:
  
  
  
  
  
  • Since $a > 0$ and $b < 0$, $a - b > 0$, so $|a - b| = a - b$.
  
  
  
  • This is not equal to $a + b$.
  
  
  
  
  
  



• 
  
  b) $|b| - |a|$:
  
  
  
  
  
  • $|b| - |a| = -b - a = -(a + b)$.
  
  
  
  • This is the negative of $a + b$, not equal to $a + b$.
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