To solve tricky inequalities easily, students can use some helpful strategies:

1. Know the Inequality Symbols:

   • Get to know the symbols:
     • $>$ means "greater than,"
     • $<$ means "less than,"
     • $\geq$ means "greater than or equal to," and
     • $\leq$ means "less than or equal to."
   • Understanding these symbols is important for finding the right answers.

2. Isolate the Variable:

   • Start by getting the variable by itself on one side, just like you do with equations.
   • For example, to solve $3x - 5 < 7$, first add 5 to both sides:
     • This gives you $3x < 12$.
   • Then, divide both sides by 3 to find $x < 4$.

3. Reverse the Inequality:

   • When you multiply or divide both sides by a negative number, you need to flip the inequality sign.
   • For example, if you have $-2x > 6$, when you divide both sides by -2, it changes to $x < -3$.

4. Graphing Solutions:

   • Drawing your solutions on a number line can really help.
   • Use an open circle for numbers that are not included (like $x < 4$) and a closed circle for numbers that are included (like $x \leq 4$).

5. Check Your Solutions:

   • Always put your answer back into the original inequality to see if it works.
   • This step helps make sure your answer is correct and helps you understand better.

6. Practice with Different Problems:

   • Try solving various types of inequalities regularly.
   • Studies show that practicing consistently can improve how well you remember and solve problems by up to 30%.

By using these strategies, students can feel more confident and get better at solving complex inequalities.