16. If $$ |t+1|t-9 $$. a) true b) false

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16. If $$ |t+1|<8 $$, then $$ 7>t>-9 $$. a) true b) false

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1. We start with the inequality: $$ |t+1| < 8 $$ 2. This absolute value inequality can be rewritten as a compound inequality: $$ -8 < t+1 < 8 $$ 3. Subtract $$1$$ from all three parts of the inequality: $$ -8 - 1 < t+1 - 1 < 8 - 1 $$ which simplifies to: $$ -9 < t < 7 $$ 4. The statement given in the problem is $$7 > t > -9$$, which is equivalent to: $$ -9 < t < 7 $$ Since the two statements are equivalent, the answer is: a) true The statement $$7 > t > -9$$ is true for the inequality $$|t+1| < 8$$.

16. If \( |t+1|<8 \), then \( 7>t>-9 \). a) true b) false

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