# Absolute Value Inequalities

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- |t| > 7 Means t can equal 8, 9 and so on because they are larger than 7.

7 > -8 or -9 or -10 and so on. However |-8| > 7 So can t = -8?

Therefore what values can t be? answer

- |t| < 7 Means t can equal 6, 5 and so on because they are smaller than 7.

-8 < 7 as are -9 or -10 and so on. However |-8| = 8 > 7 So can t = -8?

Therefore what values can t be? answer

If ≥ is substituted for > in |t| > 7 so it appears as this |t| ≥ 7 then t __can be__ 7 or larger
or -7 or less.

This is written t ≤ -7 or t ≥ 7 or as (-∞, -7] [7,∞) The bracket mean that t can be 7 or -7

If ≤ is substituted for < in |t| < 7 so it appears as this |t| ≤ 7 then t __can be__ 7
or -7 or any value between them, such as -6 etc.

This is written -7 ≤ t ≤ 7 or as [-7,7] The bracket mean that t can be 7 or -7

Always try to solve the problem before looking at the answer.

Try these problems and remember always try to solve the problem before looking at the answer:

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