If a and b are real numbers such that a > 0 and b < 0, then which of the following is equivalent to |𝑎|−|𝑏| ?
Question
If a and b are real numbers such that a > 0 and b < 0, then which of the following is equivalent to |𝑎|−|𝑏| ?
Solution
The expression |𝑎|−|𝑏| can be simplified based on the given conditions a > 0 and b < 0.
Since a > 0, the absolute value of a, |a|, is simply a.
Since b < 0, the absolute value of b, |b|, is -b (because the absolute value of a number is its distance from zero on the number line, regardless of direction).
So, |𝑎|−|𝑏| is equivalent to a - (-b), which simplifies to a + b.
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