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How do you solve the inequality: # abs(x + 2) < 18#?

Answer 1

Genesis Allen

#x<16#
#x> -20#

#abs(x+2)<18#

Separate the inequality into two inequalities, one positive and one negative.

#x+2<18 and -(x+2)<18#

Positive Inequality

#x+2<18#

Subtract #2# from both sides.

#x<18-2##=#

#x<16#

Negative Inequality

#-(x+2)<18#

#-x-2<18#

Add #2# to both sides.

#-x<18+2##=#

#-x<20#

Multiply both sides times #-1#.

#x> -20#

Solutions for #x#.

#x<16# #x> -20#

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Answer 2

Kennedy Adams

To solve the inequality ( |x + 2| < 18 ), first isolate the absolute value expression by considering two cases:

( x + 2 \geq 0 ): In this case, the absolute value expression simplifies to ( x + 2 ), so the inequality becomes ( x + 2 < 18 ). Solve for ( x ).
( x + 2 < 0 ): In this case, the absolute value expression simplifies to ( -(x + 2) ), so the inequality becomes ( -(x + 2) < 18 ). Solve for ( x ).

Combine the solutions from both cases to find the overall solution set for the inequality.

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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 the inequality: # abs(x + 2) &lt; 18#?

How do you solve the inequality: # abs(x + 2) < 18#?