How do you solve and graph the compound inequality #5 < 4x + 1 < 13# ?

Answer 1

You could break this up into 2 separate inequalities, but there probably is no real advantage to this.

Remember that you can perform the following operations without modifying the orientation of the inequality:
1. Add or Subtract any value.
2. Multiply or Divide by any value #>0#

#5 < 4x+1 < 13#

#4 < 4x < 12 # after subtracting 10 from each expression

#1 < x < 3# after dividing each expression by 4

Graphed as a number line this would look like:

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Answer 2

Eli Assouline

To solve and graph the compound inequality 5 < 4x + 1 < 13, first, subtract 1 from each part of the compound inequality: 4 < 4x < 12. Then, divide each part by 4: 1 < x < 3. To graph this solution on a number line, draw a closed circle at 1 and a closed circle at 3, and shade the region between them.

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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 graph the compound inequality #5 &lt; 4x + 1 &lt; 13# ?

How do you solve and graph the compound inequality #5 < 4x + 1 < 13# ?