Simplifying Absolute Value Express the quantity without using absolute value. a+b+|a−b|,where a&lt;b

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Simplifying Absolute Value Express the quantity without using absolute value. a+b+|a−b|,where a&amp;lt;b

timbalemX · Accepted Answer

Given:  A value is lower than B value.  Calculation:  The absolute value of a real number x is,  {x, if x≥0−x, if x&amp;lt;0  The value of a is less than b, so the subtraction will result in a negative value.  |a−b|=−(a−b)=b−a (1)  Use the value of |a−b| from equation (1), the quantiny a+b+|a−b| is,  a+b+|a−b|=a+b+b−a=2b  The quantity a+b+|a−b| without using the absolute value is 2b.

user_27qwe · Accepted Answer

To simplify the expression a+b+|a−b|, where a&amp;lt;b, without using absolute value, we can consider two equation: when a−b is positive and when a−b is negative.Equation 1: a−b&amp;gt;0In this equation, |a−b|=a−b. Substituting this into the expression, we have:a+b+|a−b|=a+b+(a−b).Now we can simplify by combining like terms:a+b+|a−b|=a+b+a−b.Rearranging the terms:a+b+|a−b|=2a.Therefore, when a−b&amp;gt;0, the expression simplifies to 2a.Equation 2: a−b&amp;lt;0In this equation, |a−b|=−(a−b). Substituting this into the expression, we have:a+b+|a−b|=a+b−(a−b).Simplifying by combining like terms:a+b+|a−b|=a+b−a+b.Rearranging the terms:a+b+|a−b|=2b.Therefore, when a−b&amp;lt;0, the expression simplifies to 2b.

Jazz Frenia · Accepted Answer

Answer:simplified&amp;nbsp;expression={2a,if&amp;nbsp;a−b&amp;gt;02b,if&amp;nbsp;a−b&amp;lt;0Explanation:To express the quantity a+b+|a−b| without using absolute value, we need to consider two cases: when a−b is positive and when a−b is negative.Case 1: a−b&amp;gt;0In this case, |a−b|=a−b, so the expression becomes a+b+(a−b). We can simplify this further:a+b+(a−b)=a+b+a−b=2aCase 2: a−b&amp;lt;0When a−b is negative, |a−b|=−(a−b). Therefore, the expression becomes a+b−(a−b). Simplifying this, we have:a+b−(a−b)=a+b−a+b=2bTherefore, the simplified expression, without using absolute value, is:simplified&amp;nbsp;expression={2a,if&amp;nbsp;a−b&amp;gt;02b,if&amp;nbsp;a−b&amp;lt;0

Simplifying Absolute Value Express the quantity without using absolute value.a+b+|a-b|,where a<b

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