Question

Rewrite without absolute value for the given conditions:
y=|x−5|+|x+5|, if x<−5

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Without absolute value for the given conditions:

y=|x−5|+|x+5|, if x<−5 is equal to  -2x

• We know absolute vale gives positive output.

• Therefore if an expression is negative inside the absolute modulus sign, it changes it so as to give a positive value.

For example , imagine x < a.

• If x is less than a then x - a will be negative.
• So | x - a | to give a positive value it should be changed to a - x .
• Since a is greater than x , a - x will be positive.

Now addition inside modulus sign, |x + a | compares x with -a .

• That is | x +a | can be written as | x - (-a) |.
• If x > -a , then this is positive
• else if  x < -a,  it should be changed to -a -x to be positive.

Now in the question, x is less than -5. SO obviously x is less than 5.

• Therefore | x -5 | should be changed to 5 - x to get positive value.

• Also | x - (-5) | should be changed to -5 -x to get positive value.
• Therefore y = 5 - x + -5 - x = -2x

Therefore without absolute value , for x <-5, y = -2x