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How do you solve #|- 10x - 5| = 0#?

Answer 1

See a solution process below:

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent. However, because #-0# equals #0# we can just solve the term within the absolute value function once for #0#:

#-10x - 5 = 0#

#-10x - 5 + color(red)(5) = 0 + color(red)(5)#

#-10x - 0 = 5#

#-10x = 5#

#(-10x)/color(red)(-10) = 5/color(red)(-10)#

#(color(red)(cancel(color(black)(-10)))x)/cancel(color(red)(-10)) = -1/2#

#x = -1/2#

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Answer 2

Kennedy Adams

To solve the equation ( |-10x - 5| = 0 ), set the expression inside the absolute value equal to zero: ( -10x - 5 = 0 ). Then, solve for ( x ): ( -10x = 5 ), ( x = -\frac{1}{2} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.