How do you solve and write the following in interval notation: #abs(2x+9) ≤ 3#?

Answer 1

Genesis Allen

The solution is #x in [-6,-9/2] uu[-9/2,-3]#

This equation has two solutions.

#2x+9<=3# and #-2x-9<=3#

#2x<=-6# and #2x>=-12#

#x<=-3# and #x>=-6#

We must find a solution to

#2x+9=0#

#x=-9/2#

Consequently, the answers are

#x in [-6,-9/2] uu[-9/2,-3]#

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Answer 2

Eva Adamson

To solve the inequality ( |2x+9| \leq 3 ) and write the solution in interval notation, follow these steps:

Set up two inequalities: ( 2x+9 \leq 3 ) and ( -(2x+9) \leq 3 ).
Solve each inequality separately for ( x ).
Write the solutions in interval notation.

Solutions:

For ( 2x+9 \leq 3 ): ( 2x \leq -6 ) ( x \leq -3 )
For ( -(2x+9) \leq 3 ): ( -2x - 9 \leq 3 ) ( -2x \leq 12 ) ( x \geq -6 )

Combine the solutions: [ x \in [-3, -6] ]

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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.