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How do you solve #|d+5|>2#?

Answer 1

Kennedy Adams

#-2 < d > -7#

#abs(d + 5) > 2#

#d + 5 > 2 or d + 5 > - 2#

#d + 5 > 2#

Subtract #5# from both sides;

#d + 5 - 5 > 2 - 5#

#d > -3#

In the same way.

#d + 5 > - 2#

Subtract #5# from both sides;

#d + 5 - 5 > - 2 - 5#

#d = > -7#

Consequently,

#-2 < d > -7#

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Answer 2

Eli Assouline

To solve the inequality ( |d + 5| > 2 ), follow these steps:

Split the inequality into two cases: ( d + 5 > 2 ) and ( d + 5 < -2 ).
Solve each case separately.
Combine the solutions.

Case 1: ( d + 5 > 2 ) [ d + 5 > 2 ] [ d > 2 - 5 ] [ d > -3 ]

Case 2: ( d + 5 < -2 ) [ d + 5 < -2 ] [ d < -2 - 5 ] [ d < -7 ]

Combine the solutions: [ -7 < d < -3 ]

So, the solution to the inequality is ( -7 < d < -3 ).

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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.

How do you solve #|d+5|&gt;2#?

How do you solve #|d+5|>2#?