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How to Graph Combined Inequalities

An inequality symbol indicates the size relationship between a term to its left and a term to its right. The inequality symbols are > ("greater than"), < ("less than"), ≥ ("greater than or equal to") and ≤ ("less than or equal to"). A combined, or compound, inequality involves two critical numbers separated by a variable. For example, x > 2 is a simple inequality but -4 < x > 2 is a combined inequality.

Instructions

- 1
  Graph the combined inequality 6 ≤ x ≤ 12 on a number line. Note that this could be read as "6 is less than or equal to x and 12 is greater than or equal to x", meaning that x falls between the two numbers and the inequality thus represents an intersection.
- 2
  Draw a number line and label the integers, placing 0 at the far left and labeling the whole numbers up to 12, because the inequality states that the value must be larger than 6 and smaller than 12.
- 3
  Draw closed, or filled in, circles on the 6 and on the 12 to represent the "equals to" possibility of the inequality symbols. Shade in the section of number line between the dots to represent the intersecting solution set for "x."

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