Variables are very important for understanding linear equations and inequalities. They help us show unknown amounts that can change.

Think about a simple linear equation like this:

[ y = 2x + 3. ]

In this equation, the letter ( x ) is the variable. It can be any number, and because of that, ( y ) will also change based on what ( x ) is.

When we solve equations, we change these variables to find out what they are. For example, if we say that ( y = 11 ), we can plug that into our equation:

[ 11 = 2x + 3. ]

Now, we want to find out what ( x ) is. When we do the math, we can find out that ( x ) equals 4.

Now, let’s talk about inequalities. These are a bit different. Variables in inequalities help us show ranges of numbers. For example, if we write ( x > 5 ), it means ( x ) can be any number that is bigger than 5. So, there is a whole bunch of possible answers.

In short, variables are the key to understanding and solving both equations and inequalities. They help us describe relationships between numbers and find answers.