How do you solve and graph the compound inequality #-2< 2 x - 4 < 6#?

Answer 1

#x \in ]1, 5[#

#- 2 + 4 < 2x < 6 + 4#
#(- 2 + 4)/2 < x < (6 + 4)/2#
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Answer 2

To solve the compound inequality -2 < 2x - 4 < 6, first add 4 to all parts of the inequality to isolate 2x. This gives us 2 < 2x < 10. Then, divide all parts by 2 to solve for x. So, 1 < x < 5. To graph this solution on a number line, draw a closed circle at 1 and another closed circle at 5, since x is strictly greater than 1 and strictly less than 5. Then shade the region between the two closed circles.

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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.

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.

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.

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.

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