Solving Multi-step Inequalities
Solving inequalities is very similar to solving equations. The goal is to isolate the variable on one side of the inequality symbol.
Here's an example:
- x + 7 ≥ 9 [In words, "some number plus 7 is greater than or equal to 9."]
- To solve, subtract 7 from both sides: x + 7 − 7 ≥ 9 − 7
- You are left with x ≥ 2, "x is greater than or equal to 2"
There is one important thing to remember about solving inequalities, however: multiplying or dividing both sides by a negative number reverses the sign. In other words, ≥ becomes ≤, < becomes >, and so forth. So, for example, the inequality -2x > 10 has a solution of x < -5.
One last note of caution: if the variable moves from one side of the inequality symbol to the other, the inequality symbol should be reversed. Don't be confused if the solution is 20 ≥ n but the correct answer is given as n ≤ 20: these expressions mean the same thing!