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How do you solve and write the following in interval notation: #−4 <2x − 3<4#?

Answer 1

Hazel Anglin

#-1/2 < x < 7/2#

Ad 3 to everything

#-4+3<2x-3+3<4+3#

#-1<2x<7#

Divide every thing by 2

#-1/2 < x < 7/2#

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Answer 2

Eva Abramson

To solve and write the inequality −4 < 2x − 3 < 4 in interval notation, first, add 3 to all parts of the inequality to isolate 2x. This gives us -1 < 2x < 7. Then, divide all parts by 2 to solve for x, resulting in -1/2 < x < 7/2. Finally, express the solution in interval notation, which is (−1/2, 7/2).

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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 and write the following in interval notation: #−4 &lt;2x − 3&lt;4#?

How do you solve and write the following in interval notation: #−4 <2x − 3<4#?