How to Solve Multi-Step Inequalities Easily

Solving inequalities can be tricky, but with some clear strategies, you can do it better. Here are some simple steps to help you:

1. Know the Inequality Symbols:

   • It's important to understand what each symbol means:
     • $>$ means "greater than"
     • $<$ means "less than"
     • $\geq$ means "greater than or equal to"
     • $\leq$ means "less than or equal to"

2. Get the Variable Alone:

   • Start by simplifying the inequality. This is similar to solving an equation. The goal is to get the variable by itself on one side.
   • For example, with the inequality $3x + 5 < 11$, you would subtract 5 from both sides. This gives you $3x < 6$. Then, divide by 3 to find $x < 2$.

3. Combine Like Terms:

   • Make sure to put all similar terms together. This helps make the equation simpler, reducing mistakes.

4. Flip the Inequality When Needed:

   • Remember, if you multiply or divide by a negative number, you have to flip the inequality symbol. For instance, if you have $-2x > 6$, dividing by -2 means you change it to $x < -3$.

5. Check Your Answers:

   • Always put your answer back into the original inequality to make sure it works. This way, you can be sure your solution is correct.

By following these steps, you'll find it easier to work through multi-step inequalities. This will help you understand algebra better and feel more confident in your math skills!