The Triangle Inequality: Given a = 5 and b = −3, verify that the triangle inequality |a+b|≤|a|+|b| holds.

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braodagxj · Accepted Answer

Step 1  In words triangle inequality states that absolute value of sum of two quantities is less than or equal to sum of absolute value of the two quantities. For a non-negative number absolute value is equal to the number itself.  For a negative number the absolute value is the negative of the number. Evaluate both sides of the inequality and check if it holds.  Step 2  Given numbers are a=5,b=−3. First compute |a+b|.  |a+b|=|5-3|  =|2|  =2  Now compute |a|+|b|  |a|+|b|=|5|+|-3|  =5+3  =8  Calculation shows that |a+b|&amp;lt;|a|+|b|. Hence, triangle inequality is satisfied for given numbers.

The Triangle Inequality: Given a = 5 and b =

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