Algebra Calculator: Solve Equations Step by Step

An Algebra Calculator can be a useful tool to help students, teachers and professionals solve algebraic equations easily and accurately. This can be used to solve various algebraic equations including linear equations, simplification and factorising polynomials.

Algebra is an important area of mathematics using letters, numbers, symbols and operations. Letters are often used to represent unknown values such as x, y and z. Algebraic problems are solved by finding the value of these variables.

Our free Algebra Calculator can help solve various problems quickly. Simply type in an equation and the calculator will show you the answer in seconds.

Students in the United States can use this calculator to help with their algebra homework, revision for exams at school, SAT or ACT revision and general maths revision.

You can use the Algebra Calculator online whether you’re learning basic algebra or more complicated equations.

How to use the Algebra Calculator

It’s very easy to use an online Algebra Calculator. You don’t need any advanced knowledge or specialist software.

Simply follow the steps below to solve an algebraic problem:

Enter your equation. Type in your algebraic equation or expression. For example, 2x + 5 = 15.

Ensure your expression is correct. Ensure you have used the correct numbers, letters, operations and equals signs.

Click calculate. Click ‘Calculate’ or ‘Solve’.

See your answer. The calculator will show you the answer.

Review calculation. If there are step by step calculations shown you can see how the answer was reached.

Try another equation. Use the ‘Reset’ option to clear the last calculation. Then type in a new question.

If you type in 2x + 5 = 15 the calculator will solve for x.
Answer:

x = 5

This makes it easier to solve algebraic problems.

Algebra Calculator Formula

There is no specific formula for all algebraic problems as there are many types of equations. Depending on the problem you are trying to solve you need to use the correct formula.

Here are some formulas commonly used in algebra.

Linear Equation Formula

This is the general formula for a single variable linear equation:
ax+b=c
To find the value of x:
x = (c – b)/a
Where,
a = Coefficient
b = Constant
c = The value on the right hand side
x = Unknown
Quadratic Equation Formula
This is the standard formula for a quadratic equation:
ax^2+bx+c=0
x = (-b ± √(b2 – 4ac))/2a
This can be used to calculate the roots of a quadratic equation.
Slope Formula
The slope of a straight line can be calculated by:
m = (y2 – y1)/(x2 – x1)
Where m is the slope and the coordinates are \\((x_1,y_1)\\) and \\((x_2,y_2)\\).
Basic Algebraic Identity
A common identity used is:
(a + b) 2=a^2 + 2ab + b2
These formulas can be used to solve various algebraic problems in maths, science, engineering and everyday calculations.

Example Calculation

Let’s look at an example to see how the Algebra Calculator works.
Question:
Solve:
3x + 7=22
Solution:
Write out the equation.
3x + 7=22
Subtract 7 from both sides.
3x = 22 – 7
3x = 15
Divide both sides by 3.
x = 15/3
Calculate the answer.
5 = 150__
Answer: 5 = 151__
Check:
Substitute in 5 = 152__.
3(5) + 5 = 153__
5 = 154__
5 = 155__

As both sides are equal this is correct.

This shows how we can solve an algebraic equation using basic mathematical operations.

Understanding your answer

Your answer will show you the solution to the problem you’ve typed in.
Depending on what type of calculation you’ve done your answer could be:
Single variable: Shows you the value of the unknown variable, such as 5 = 156__.
Multiple answers: Some equations have more than one answer.
Simplified: Shows you the simplified equation.
Factored: Shows you the factored equation.
Decimal: Shows you the value as a decimal.
Fraction: Shows you the exact value as a fraction.
No solution: Shows you there is no solution to the equation.
Infinite solutions: Shows you there are infinite solutions.
For example, the quadratic equation:
x2 – 5x + 5 = 157__
Has 2 solutions:
5 = 158__ or 5 = 159__

This helps you to understand how many solutions your equation has.

What affects your answer?

There are many factors which can affect your answer. Knowing these can help you enter your problems correctly and avoid errors.

Correct equation

If you type in the wrong equation or miss out an operation you may get an unexpected answer. Double check your equation.

Mathematical operations

Make sure you use the right operations such as addition, subtraction, multiplication, division and exponents. Changing your operation can change your answer completely.

Brackets

Brackets will change the order of your operations. For example 2(x + 3) is different to 2x + 3.

Coefficients and constants

Coefficients are numbers multiplied by a variable. Constants are fixed numbers. If you enter them incorrectly your answer may be affected.

Type of equation

There are various types of equations such as linear, quadratic, polynomial and simultaneous equations. Make sure your calculator can solve the equation you’re using.

Domain

Some equations include fractions, square roots and logs which mean there are restrictions on what the variable can be.

Rounding

Answers may be rounded. Getting the exact fraction or symbol can give a more accurate answer.

Advantages and uses

There are many advantages to using an online Algebra Calculator.
Saves time: Solving algebraic equations can take several minutes but using an online calculator can give you an answer much quicker.

• Helps students: Students can use this to check their answers to homework, practice equations and understand maths.
• Helps with SAT/ACT: Algebra is an important topic in US standardised maths tests. This can help students revise equations and check practice problems.
• Minimises errors: Using an automated calculator can help reduce errors but make sure your equation is correct.
• Improves understanding: Comparing your answers to the calculator can help students understand where they went wrong.
• Helps teachers: Teachers can use algebra calculations when creating examples, worksheets, assignments and practice questions.
• Helps professionals: Engineers, scientists, analysts and many other professionals use algebraic concepts.
• Can be used online: This calculator can be used on computers, tablets and smartphones.

Accuracy, Assumptions and Limitations

If you type in an equation correctly and your calculator can perform the calculation you want then you can get an accurate answer.

However, there are some important assumptions and limitations to know:

• Correct input: The calculator will give you an answer based on what you input. If you use wrong symbols, miss out numbers or make a mistake with formatting you may get an incorrect or unexpected answer.
• Not all calculators can do complex calculations: Not all algebra calculators can perform complex calculations. Some only do basic linear and quadratic equations.
• Rounding: Answers may be rounded.
• Domain: Some equations have domain restrictions. These can include dividing by zero, negative numbers inside real square roots or logs.
• Complex numbers: Some equations have complex number answers which may not show up on calculators which only do real numbers.
• Step-by-step: Some calculators give full step-by-step answers whereas others just give the final answer.
• Learning: The calculator should help you learn. It’s best to practice solving equations manually.

Check important work using mathematical rules or a different method.

FAQ

What is an Algebra Calculator?

An Algebra Calculator is an online maths tool used to solve algebraic equations. It can help you find unknown variables, solve linear and quadratic equations and perform other algebraic operations depending on the calculator.

Is it free?

Many Algebra Calculators online are free to use. You can enter maths expressions, solve equations and check your answers without paying for expensive software.

Can it solve quadratic equations?

Yes! If your Algebra Calculator can solve quadratic equations it can solve equations in the form x = 50__. Using the quadratic formula or other methods it can calculate the roots.

Can I use it for schoolwork?

Yes! Students can use this to check answers to homework, practice equations and understand maths. However it’s best to try and learn how to solve the equations.

Does it work on mobiles?

Most Algebra Calculators online will work on your smartphone, tablet, laptop and desktop. Just open the calculator in a modern browser.