## 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 -2*x* > 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!