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How do you solve #|8r - 3| <67#?

Answer 1

Isaiah Anthony

To solve the inequality |8r - 3| < 67:

Set up two inequalities: 8r - 3 < 67 and - (8r - 3) < 67.
Solve each inequality separately.
Combine the solutions to find the range of values for r.

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Answer 2

Julia Adams

The solution to this problem is the interval:

#-8 < r < 35/4#

Because this is an absolute value inequality we must convert this to an inequality set and solve the inequality set while keeping the set balanced:

#-67 < 8r - 3 < 67#

#-67 + 3 < 8r - 3 + 3 < 67 + 3#

#-64 < 8r < 70#

#-64/8 < (8r)/8 < 70/8#

#-8 < r < (2/2) (35/4)#

#-8 < r < 35/4#

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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 #|8r - 3| &lt;67#?

How do you solve #|8r - 3| <67#?