Introduction
This algebra calculator solves math problems and shows you every step. Type a problem like 4x+2=2(x+6) or x^2-5x+6=0, then press Calculate. You get the answer, the steps, and a graph.
You can do a lot with it:
- Solve equations for x, including quadratics with real or complex answers
- Simplify and expand expressions, or factor them
- Evaluate an expression when you know the values of the variables
- Inequalities with <, >, ≤, and ≥, shown on a number line
- Systems of equations using elimination, substitution, or Cramer's Rule
- Graph your equation and see where it crosses the axes
There is also a "More Actions" menu for things like degree, intercepts, vertex, domain, and the discriminant. If you are not sure how to type a symbol, open the keypad and tap it. Want to check your own work? Type your answer in the "Check Your Answer" box and the tool will tell you if it matches.
Use it for homework, test review, or just to see how a problem works step by step.
How to use our Algebra Calculator
Type an algebra problem, pick what you want done with it, and the calculator shows the answer, step-by-step work, a graph, and a number line.
Expression or equation: Type your problem here, like 4x+2=2(x+6) or x^2-9. Use + - * / ^ , sqrt(x) for square roots, |x| for absolute value, and commas to list more than one equation. The preview under the box shows how your problem looks in math form.
Clear button (×): Press the × inside the box to erase what you typed and start again.
New Problem: Clears the input and all past results so you can enter a fresh question.
Show Keypad: Opens buttons for numbers, x, y, z, powers, roots, fractions, and signs. Tap "Full Pad" for extras like ≤, ≥, ln, and log.
Example problems: Click any example chip to drop that problem into the box. Click "Show More Examples" for a longer list.
Quick action buttons: Tap Simplify, Solve for x, Expand, Factor, Evaluate, or Graph to run that job right away. "More Actions" adds degree, leading coefficient, intercepts, vertex, completing the square, domain, and discriminant.
Tabs: Pick the tab that matches your job: Solve, Solve for Variable, Simplify, Expand, Factor, Evaluate, Inequalities, Systems, or Graph.
Include complex solutions (Solve tab): Leave this checked to see imaginary answers with i. Uncheck it to see only real answers.
Solve for (Solve for Variable tab): Choose which letter to get by itself, such as y in ax+by=c.
Variable values (Evaluate tab): Type a number for each letter the calculator finds, like x = 5 and y = 3. You can also write values after an @ sign in the main box.
Show variable sliders: Check this to drag a slider for each letter and watch the answer change as you move it.
Method (Systems tab): Choose Elimination, Substitution, or Cramer's Rule to see the steps solved that way.
X min, X max, Y min, Y max (Graph tab): Set how far the graph goes left, right, down, and up, then press "Redraw Graph".
Calculate: Press this to get your answer and the full step-by-step solution.
Reset: Puts the calculator back to its starting problem and settings.
Answer form: Switch between exact, decimal, factored, or interval forms of the answer, then press "Copy Result" to save it.
Check Your Answer: Type your own answer, like x=2, x=3, and press Verify to see if it matches the solution.
What Is Algebra?
Algebra is math that uses letters, like x or y, to stand for numbers you do not know yet. Those letters are called variables. Your job is to find what number the letter stands for, or to write the math in a simpler way.
Key Words to Know
- Term: one piece of a math problem, like 3x or 7.
- Coefficient: the number in front of a variable. In 5x, the 5 is the coefficient.
- Expression: math with no equals sign, like 2x + 4.
- Equation: math with an equals sign, like 2x + 4 = 10.
- Inequality: math that uses <, >, ≤, or ≥ instead of equals.
- Like terms: terms with the same letter and power, like 3x and 5x. You can add them.
Common Algebra Jobs
Solve means find the value of the variable. Keep the equation balanced: whatever you do to one side, do to the other side too.
Simplify means make it shorter by adding like terms and cutting extra brackets.
Expand means multiply things out. For example, 2(x + 3) becomes 2x + 6. This uses the distributive property.
Factor is the opposite of expand. You break the math into parts that multiply together, like x² − 5x + 6 = (x − 2)(x − 3).
Evaluate means put in a number for each letter and work out the answer.
Types of Equations
- Linear: the highest power is 1, like 4x + 2 = 10. Its graph is a straight line. It has one answer.
- Quadratic: has an x², like x² − 5x + 6 = 0. Its graph is a U shape called a parabola. It can have two answers, one answer, or no real answers.
- Cubic and higher: has x³ or more. It can have more answers.
- System: two or more equations at once, like x + y = 5 and x − y = 1. The answer is the point where the lines cross.
The Quadratic Formula
For any equation shaped like ax² + bx + c = 0, the answers are x = (−b ± √(b² − 4ac)) / 2a. The part under the square root, b² − 4ac, is called the discriminant. If it is positive, there are two real answers. If it is zero, there is one. If it is negative, the answers are imaginary numbers.
Order of Operations
Always work in this order: parentheses, exponents, multiply and divide (left to right), then add and subtract (left to right). People remember it as PEMDAS.
Tips That Help
- Check your answer by putting it back into the first equation. Both sides should match.
- When you multiply or divide an inequality by a negative number, flip the sign.
- A fraction can never have zero on the bottom. Toss out any answer that makes the bottom zero.
- Do one step at a time and write each step down. It makes mistakes easy to spot.
Why Algebra Matters
Algebra helps you solve real problems: working out a budget, finding a missing measurement, comparing phone plans, or changing a recipe. It is also the base for geometry, trigonometry, science, coding, and money math later on.