When I first learned about inequalities in Year 10, I felt a little confused.

Inequalities can seem tough at first, but once you understand the basic ideas, they get easier.

Here are some tips and tricks I found that can help you with inequalities:

1. Know the Symbols

First, it’s important to learn the inequality symbols:

• $<$ means "less than"
• $>$ means "greater than"
• $\leq$ means "less than or equal to"
• $\geq$ means "greater than or equal to"

These symbols show how two numbers relate to each other, just like an equal sign. Knowing what each symbol means is key for solving inequalities.

2. Think of Inequalities Like Equations

One good tip I got was to treat inequalities like equations.

Most of the time, you can do the same things on both sides of the inequality:

• Adding or subtracting: If you add or subtract the same number to both sides, the inequality still works. For example, if you have $x + 3 > 5$, you can subtract 3 from both sides to get $x > 2$.

• Multiplying or dividing by a positive number: If you do this, the inequality stays the same. So, if you have $2x < 10$, dividing by 2 gives you $x < 5$.

3. Be Careful with Negative Numbers

Things get a bit tricky here.

If you multiply or divide both sides of an inequality by a negative number, you have to flip the direction of the inequality sign.

For example, if you start with $-3x > 9$ and you divide by -3, it becomes $x < -3$.

This rule is very important, so make sure to practice it!

4. Simplifying Expressions

Inequalities often have expressions that can be simplified. Use these methods:

• Combining like terms: Just like in regular math, combine similar parts to make the inequality clearer. For example, $2x + 3x < 10$ can be simplified to $5x < 10$.

• Factoring: When you can, factor expressions to find answers more easily. For instance, if your inequality is $x^2 - 4 < 0$, you can factor it to $(x - 2)(x + 2) < 0$.

5. Using Test Values

When dealing with compound inequalities, using test values can help.

For example, with $-2 < 3x + 1 < 5$, break it down into two parts and try different numbers to see which ranges work. This can help you figure out which values satisfy both parts of the inequality.

6. Graphing Inequalities

Drawing inequalities on a number line can be really useful.

For example, if you have $x \geq 2$, you would shade all the numbers to the right of 2, including 2 itself. This gives you a clear image of the solution, making it easier to understand.

Conclusion

In short, simplfying inequalities can be easier than you think!

Get to know the symbols, treat them like equations, be careful with negative numbers, simplify expressions, use test values, and remember to graph.

With practice and some patience, you'll get more confident with inequalities in no time!

Remember, it’s all about practice and really understanding the basics. Good luck with your studies!