Algebraic Equations

An equation is a mathematical statement that expresses the equality of two expressions. The goal of an equation is to find the value of the unknown (variable) that makes the statement true.

In this equation, x is the unknown. If x = 4, then the equation is true because 4 + 3 = 7.

Basic Concepts of Equations

• Left side (LHS – Left Hand Side): the expression on the left side of the equation.
• Right side (RHS – Right Hand Side): the expression on the right side of the equation.
• Solution: the variable value at which LHS = RHS.
• Solution set: all values that satisfy the equation.

Linear Equations

In a linear equation, the highest power of the variable is 1. These are solved most simply by a sequence of basic steps.

Solution: subtract 5 from both sides (2x = 6), then divide by 2 (x = 3).

Quadratic Equations

In a quadratic equation, the variable appears squared. General form: ax² + bx + c = 0, where a ≠ 0. Solution formula:

Example: x² - 5x + 6 = 0 → solutions: x = 2 and x = 3.

Inequalities

Inequalities are similar to equations but contain <, >, ≤ or ≥ signs. Example: 2x + 1 > 7 → solution: x > 3.

Equations in Everyday Life

• If a product's price is x forints, and you buy two, you pay 2x forints in total.
• If a car travels y km/h and covers 150 km in 3 hours, the equation is: 3y = 150 → y = 50.
• If you have 10 apples and give away z, you have 10 - z apples left.

Practice Exercise