Algebra Calculator

How to Use This Algebra Calculator

This algebra calculator helps you evaluate mathematical expressions and verify your solutions quickly. Follow these steps:

1. Enter your expression in the input field using standard notation. Use * for multiplication, / for division, and ^ for exponents.
2. Use parentheses to group terms and control the order of operations, for example (3+2)*5.
3. Click "Solve" to evaluate the expression and see the result.
4. Check your answer against the displayed solution. If you see an error message, review your expression for invalid characters or syntax.

Understanding Algebra

What Is Algebra?

Algebra is a branch of mathematics that uses letters (called variables) to represent unknown quantities. Instead of working only with specific numbers, algebra lets you write general rules and formulas that apply to many situations. It forms the foundation for nearly all advanced mathematics, from calculus to statistics to computer science.

Variables and Expressions

A variable is a symbol (usually a letter like x, y, or z) that stands for an unknown number. An algebraic expression combines variables, numbers, and operations. For example, 3x + 7 is an expression where x is the variable, 3 is its coefficient, and 7 is a constant term.

Solving Linear Equations

A linear equation is an equation where the highest power of the variable is 1. The general form is ax + b = c. Solving means isolating the variable on one side to find its value. The strategy is to perform the same operation on both sides of the equation to keep it balanced.

Systems of Equations

A system of equations is a set of two or more equations with the same variables. To find a solution, you need to find values that satisfy all equations simultaneously. Common methods include substitution (solve one equation for a variable and plug it into the other) and elimination (add or subtract equations to cancel a variable).

Key Algebra Formulas

Solving a Linear Equation

Quadratic Formula

For any quadratic equation of the form ax^2 + bx + c = 0, the solutions are:

The expression under the square root, b^2 - 4ac, is called the discriminant. If it is positive, there are two real solutions. If it is zero, there is exactly one real solution. If it is negative, there are no real solutions (only complex ones).

Slope-Intercept Form

Worked Example: Solve 3x + 7 = 22

Let us solve the linear equation 3x + 7 = 22 step by step:

This method -- performing the same operation on both sides to keep the equation balanced -- works for any linear equation of the form ax + b = c.

Algebra Tips and Tricks

• Always simplify first. Before solving, combine like terms and simplify both sides of the equation.
• Check your solution. After finding a value for x, substitute it back into the original equation to verify it works.
• Watch for sign errors. The most common algebra mistake is dropping a negative sign. Be careful when subtracting or distributing negatives.
• Factor when possible. For quadratic equations, try factoring before resorting to the quadratic formula. It is often faster.
• Use inverse operations. Addition undoes subtraction, multiplication undoes division, and vice versa. This is the core principle for isolating variables.
• Graph to understand. Plotting an equation on a coordinate plane can give you a visual understanding of solutions. The x-intercepts of a graph are the solutions.