Linear Equations Solver
Stuck on an algebraic equation? Type it below and I'll show you step-by-step how to isolate the variable and find x!
Here is the Solution!
Balancing Steps
Final Solution
Understanding Linear Equations in One Variable
What is a Linear Equation?
A linear equation in one variable is an algebraic equation where the highest power of the variable (usually x) is exactly 1. It forms a straight line when graphed and can generally be written in the form:
The golden goal of solving a linear equation is isolation—moving everything away from the variable so that it stands completely alone on one side of the equals sign.
The Golden Rule of Balance
Think of an equation as a perfectly balanced seesaw or weighing scale. The equals sign (=) tells you that both sides have the exact same value.
- If you add a number to the left, add it to the right!
- If you subtract from one side, subtract from the other!
- Multiply or divide entire sides equally to keep the balance.
Algebraic Operations Strategy
1 Simplify & Expand Brackets
If there are any brackets, use the distributive property to expand them out first, then combine like terms on each side.
Example: 2(x + 3) = 2x + 6
2 Collect Variables
Move all terms containing variables to one side (usually the left side) by adding or subtracting them from both sides.
Example: 4x = 2x + 6 → Subtract 2x → 2x = 6
3 Isolate the Constant
Move all regular numbers (constants) over to the opposite side of the equation using inverse operations.
Example: 2x + 4 = 10 → Subtract 4 → 2x = 6
4 Divide by Coefficient
Finally, divide both sides by the number attached directly to your variable to unlock your final answer.
Example: 2x = 6 → Divide by 2 → x = 3
Common Pitfalls to Avoid
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Sign Switching Errors: When you add or subtract a term across the equals sign, remember its sign reverses. Example: In $x - 5 = 10$, you must add 5 to both sides to get $x = 15$ (not subtract!).
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Distributing Partially: When multiplying an equation or expanding parentheses, make sure the outside multiplier hits every single term inside. Example: $3(x + 4)$ turns into $3x + 12$, not $3x + 4$.