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Select the correct answer. Which number line represents the solution to |3x - 3| < 3

Select the correct answer. Which number line represents the solution to |3x - 3| &lt-example-1
User Irisshpunk
by
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1 Answer

7 votes

Answer: Choice A

Open holes at 0 and 2; shading in between.

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Work Shown:

|3x - 3| < 3

- 3 < 3x - 3 < 3

- 3+3 < 3x - 3+3 < 3+3

0 < 3x < 6

0/3 < 3x/3 < 6/3

0 < x < 2

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Step-by-step explanation:

The rule to use is when |x| < k, then -k < x < k where k is positive.

After that rule is used, I added 3 to all sides and then divided all sides by 3 to isolate x.

The graph of 0 < x < 2 will have open holes at 0 and 2; then shade in between those open holes.

This describes "x is anything between 0 and 2 excluding both endpoints".

Therefore, we'll go for answer choice A

Choice C is close, but the endpoints should be open holes to indicate "exclude these endpoints". This means x = 0 and x = 2 are not part of the shaded solution set. If "or equal to" was part of the inequality signs, then choice C would be the answer.

User Mark Sholund
by
8.1k points

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