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How do you solve #abs(x+5)=4#?

Answer 1

Eli Assouline

You have to use the definition of #|a|#

The definition of #|a|# is: #a# if #a>=0# #-a# if #a<=0#

For example, #|5|=5#, #|-5|=5#, and #|0|=0#

So let's divide the issue into two sections:

#|x+5|>=0#; in this case #|x+5|=x+5#, and the equation is #x+5=4#, so #x=-1#

#|x+5|<0#; in this case #|x+5|=-(x+5)=-x-5#, and the equation is #-x-5=4#, so #x=-9#

The solutions are then #x=-1# and #x=-9#

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Answer 2

Kennedy Adams

To solve the equation |x + 5| = 4, you need to consider both the positive and negative cases for the absolute value.

Positive Case: x + 5 = 4 Subtract 5 from both sides: x = 4 - 5 x = -1
Negative Case: x + 5 = -4 Subtract 5 from both sides: x = -4 - 5 x = -9

So, the solutions to the equation |x + 5| = 4 are x = -1 and x = -9.

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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.