Solving Inequalities With One Unknown
The steps needed to solve almost any inequality in one unknown are similar to the ones we use for solving equations in one unknown. Step 4 is slightly modified and there is an additional step in which we graph the solution set to the inequality.
| Step 1 | D | Distribute. |
| Step 2 | C | Collect like terms on the each side of the inequality. |
| Step 3 | 0 | Undo all additions and subtractions on each side of the inequality. |
| Step 4 | 1* | Undo all multiplications and divisions on each side of the inequality. (*If you divide or multiply both sides of the inequality by some negative number, you must flip the inequality symbol.) |
| Step 5 | G | Graph the solution set. (<,> get graphed with an open dot. <,> get graphed with a closed dot.) |
Directions: Please solve for the unknown in the following inequality. Also, graph the solution set.
-3(4g+9)+2g<12
| Step 1 | Distribute | -12g-27+2g<12 | ||
| Step 2 | Collect Like Terms | -10g-27<12 | ||
| Step 3 | 0 Undo Add/Subtract | -10g<39 | ||
| Step 4 | 1* Undo Multiply/Divide | g>-3.9 | Note: flip the sign b/c we divided by -10 | |
| Step 5 | Graph |
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Directions: Please solve for the unknown in the following inequality. Also, graph the solution set.
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