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

May 9, 2015

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 $> 0$

$5 < 4 x + 1 < 13$

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

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

Graphed as a number line this would look like: