How do you solve and write the following in interval notation: #6t6<6#?
See full solution process below
Because this is a problem contain the absolute value function we must solve the problem for both the negative and positive forms of the problem or in this case +6 and 6.
Also, because it is an inequality we must solve it as a system of inequalities as shown below.
We can rewrite this problem as:
We can now solve while ensuring we perform all operations to each portion of the system of inequalities.
Writing this solution in interval form gives:
(0, 2)
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To solve the absolute value inequality 6t  6 < 6 and write it in interval notation:

Set up two separate inequalities: a) 6t  6 < 6 b) (6t  6) < 6

Solve each inequality separately: a) 6t  6 < 6 Add 6 to both sides: 6t < 12 Divide by 6: t < 2
b) (6t  6) < 6 Distribute the negative sign: 6t + 6 < 6 Subtract 6 from both sides: 6t < 0 Divide by 6 (remember to flip the inequality sign): t > 0

Combine the solutions: The solution is 0 < t < 2

Write the solution in interval notation: Interval notation: (0, 2)
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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