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How do you solve #abs[2x-2]<=13#?

Answer 1

Kennedy Adams

#-6.5<=x<=7.5#

#|2x-2|<=13# is the given inequality

So we can take,

#2x-2<=13 # -----AND----- # -13<=2x-2#

#2x-2<=13#

#2x<=15#

#x<=7.5#

#-13<=2x-2#

#-11<=2x#

#-6.5<=x#

Now since there is an and situation we will use intersection

#-6.5<=x<=7.5#

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Answer 2

Julia Adams

To solve the inequality ( |2x - 2| \leq 13 ), you can follow these steps:

Split the inequality into two separate inequalities:

( 2x - 2 \leq 13 ) and ( 2x - 2 \geq -13 )
Solve each inequality separately:

For ( 2x - 2 \leq 13 ): [ 2x - 2 \leq 13 ] [ 2x \leq 15 ] [ x \leq \frac{15}{2} ]

For ( 2x - 2 \geq -13 ): [ 2x - 2 \geq -13 ] [ 2x \geq -11 ] [ x \geq \frac{-11}{2} ]
Combine the solutions: [ \frac{-11}{2} \leq x \leq \frac{15}{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.

How do you solve #abs[2x-2]&lt;=13#?

How do you solve #abs[2x-2]<=13#?