Equation Solver Calculator
Solve linear equations step by step with detailed solutions
How to Solve Linear Equations
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The general form is ax + b = c, where a, b, and c are constants.
Steps to Solve Linear Equations
- Simplify both sides of the equation by combining like terms
- Use addition or subtraction to move all variable terms to one side
- Use addition or subtraction to move all constant terms to the other side
- Multiply or divide to isolate the variable
- Check your solution by substituting back into the original equation
Example
Solve: 3x + 7 = 22
Step 1: Subtract 7 from both sides
3x = 15
Step 2: Divide both sides by 3
x = 5
Step 3: Check by substituting x = 5
3(5) + 7 = 15 + 7 = 22 ✓
Frequently Asked Questions
What is a linear equation?
A linear equation is an equation where the highest power of the variable is 1. It graphs as a straight line and has the general form ax + b = c, where a, b, and c are constants and x is the variable.
How do you solve equations with variables on both sides?
To solve equations with variables on both sides, first collect all variable terms on one side by adding or subtracting. Then collect all constant terms on the other side. Finally, divide or multiply to isolate the variable.
What does it mean if an equation has no solution?
An equation has no solution when you end up with a false statement like 0 = 5. This means there is no value of the variable that makes the equation true. These are called contradictions.
What does it mean if an equation has infinitely many solutions?
An equation has infinitely many solutions when you end up with a true statement like 0 = 0. This means any value of the variable makes the equation true. These are called identities.
Why is it important to show your work when solving equations?
Showing your work helps you track each step, makes it easier to find errors, demonstrates your understanding of the process, and allows others to follow your reasoning. It's especially important for complex multi-step equations.
How can I check if my solution is correct?
Substitute your solution back into the original equation. If both sides equal the same value, your solution is correct. For example, if x = 5 is your solution to 2x + 3 = 13, check: 2(5) + 3 = 10 + 3 = 13 ✓
What are the common mistakes when solving linear equations?
Common mistakes include sign errors when moving terms, forgetting to distribute negative signs, dividing or multiplying only one side, and not simplifying completely before solving. Always work carefully and check your answer.
Can linear equations have fractions or decimals?
Yes, linear equations can contain fractions or decimals. You can solve them as-is, or clear fractions by multiplying by the LCD, or clear decimals by multiplying by a power of 10. The solution method remains the same.
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