Understanding Expressions and Equations

Expressions and equations are the building blocks of algebra. An expression is a combination of numbers, variables, and operators (such as + and -) that shows a value, but does not have an equal sign. An equation shows that two expressions are equal, using an equal sign (=).

Working with Variables

Variables are symbols, often letters like \( x \) or \( y \), that represent unknown numbers. You can use them to write expressions like \( 2x + 5 \) or equations like \( 2x + 5 = 11 \).

Simplifying and Solving

Simplifying expressions means combining like terms and using arithmetic to make them as simple as possible. Solving equations means finding the value of the variable that makes the equation true.

• Combine like terms: \( 3x + 4x = 7x \)
• Solve: If \( x + 4 = 9 \), subtract 4 from both sides to get \( x = 5 \).

Real-World Connections

Expressions and equations help us solve everyday problems, like figuring out totals, comparing prices, or calculating distances.

Practice Tips

• Always perform the same operation on both sides of an equation.
• Check your answer by plugging it back into the equation.