Question

What is the simplified form of the expression |x-12|+|x-14| for values of x such that 12<x<14?​

Answer 1

SOLUTION

TO DETERMINE

The simplified form of the expression

|x-12|+|x-14| for values of x such that 12<x<14

CONCEPT TO BE IMPLEMENTED

We are aware of the modulus function that

$\sf |x | = \begin{cases} & \sf{ \: \: \: \: x \: \: \: \: when \: x > 0} \\ \\ & \sf{ - x \: \: \: \: \: when \: x \leqslant 0} \end{cases}$

EVALUATION

Now the given expression is

$\sf{ |x - 12| + |x - 14| }$

Now the given inequality is

$\sf{12 < x < 14}$

$\sf{Since \: \: x > 12}$

$\sf{ \therefore \: \: |x - 12| = x - 12}$

$\sf{Since \: \: x < 12}$

$\sf{ \therefore \: \: |x - 14| = - (x - 14) = 14 - x}$

Hence the required value of the given expression is

$\sf{ |x - 12| + |x - 14| }$

$\sf{ = (x - 12) + (14 - x) }$

$= 2$

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