Multi-Step Equation Calculator
Solve complex linear equations with distribution and like terms
Try equations with parentheses, like terms, or variables on both sides
Solving Multi-Step Equations
Multi-step equations require several operations to solve. They often involve the distributive property, combining like terms, and working with variables on both sides of the equation.
Steps to Solve Multi-Step Equations
- Distribute: Remove parentheses using the distributive property
- Combine like terms: Simplify each side of the equation
- Move variables: Get all variable terms on one side
- Move constants: Get all constant terms on the other side
- Isolate the variable: Divide or multiply to solve for the variable
- Check: Substitute your answer into the original equation
Example with Distribution
Solve: 3(x + 4) = 2x + 17
Step 1: Distribute the 3
3x + 12 = 2x + 17
Step 2: Subtract 2x from both sides
x + 12 = 17
Step 3: Subtract 12 from both sides
x = 5
Variables on Both Sides
When variables appear on both sides, move them to one side by adding or subtracting.
Example: 5x - 3 = 2x + 9
Subtract 2x: 3x - 3 = 9
Add 3: 3x = 12
Divide by 3: x = 4
Frequently Asked Questions
What makes an equation "multi-step"?
A multi-step equation requires more than two operations to solve. It often includes parentheses requiring distribution, multiple like terms to combine, or variables on both sides of the equation.
What is the distributive property?
The distributive property states that a(b + c) = ab + ac. You multiply the term outside the parentheses by each term inside. For example, 3(x + 2) = 3x + 6.
How do I combine like terms?
Like terms have the same variable raised to the same power. Combine them by adding or subtracting their coefficients. For example, 3x + 5x = 8x, and 7 - 2 = 5.
Which side should I move variables to?
You can move variables to either side, but it's usually easier to move them to the side where the coefficient will be positive. This helps avoid working with negative numbers.
What if I get 0 = 0 or 5 = 5?
If you get a true statement like 0 = 0, the equation is an identity with infinitely many solutions. Any value of x makes the equation true.
What if I get 0 = 5 or 3 = 7?
If you get a false statement like 0 = 5, the equation is a contradiction with no solution. There is no value of x that makes the equation true.
Can I distribute a negative number?
Yes, when distributing a negative, multiply it by each term inside the parentheses. For example, -2(x + 3) = -2x - 6. Remember that negative times positive equals negative.
What's the most common mistake in multi-step equations?
Common mistakes include forgetting to distribute to all terms, sign errors when moving terms, and not combining all like terms before solving. Always work carefully and check each step.
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