What Are Linear Equations?

Linear equations are mathematical statements that show the relationship between variables using addition, subtraction, multiplication, or division—without exponents or squares. These equations form straight lines when graphed on a coordinate plane.

Understanding Variables and Expressions

An expression is a combination of numbers, variables (like \(x\)), and operations. For instance, \(3x + 2\) is an expression.

An equation is when two expressions are set equal, like \(3x + 2 = 8\).

Solving Linear Equations

To solve a linear equation means to find the value of the variable that makes the equation true.

Steps:

1. Simplify both sides if needed.
2. Use inverse operations to isolate the variable.
3. Check your solution by plugging it back in.

Real-World Connections

Linear equations help you figure out things like: If you earn $10 per hour, how many hours do you need to work to make $50? The equation \(10h = 50\) helps you solve for \(h\).

Practice Makes Perfect

Try writing and solving equations for different scenarios—like saving money or figuring out how many tickets you need to sell at a fundraiser.