Compound Inequalities With Or

Compound inequalities with or

A compound inequality with or means the solution can satisfy either inequality, not necessarily both. This usually creates a union of two solution sets.

1) Solve each inequality separately

Treat each part like a normal inequality. Isolate the variable using inverse operations:

• add or subtract the same number on both sides
• multiply or divide by a positive number without changing the sign
• if you multiply or divide by a negative number, reverse the inequality sign

2) Combine the results with or

Write the solution set as the values that make the first inequality true or the second inequality true. On a number line, this is the set of all points in either shaded region.

3) Simplify the final answer

Convert each part to the simplest form possible. If the two solution sets overlap, the final answer is still the union of both sets.

4) Check a value from each region

Test one number that should work for the left part and one that should work for the right part. Also test a number between the two regions to make sure it does not work if the intervals are separate.

Example pattern

If you get something like x < a or x > b, the solution is everything less than a together with everything greater than b.