Free Linear Equation Solver
Type any linear equation — one variable, two variables, or a system — and see the full step-by-step solution using inverse operations, substitution or elimination.
💡 You can also paste an image with Ctrl+V or drag a file here.
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A linear equation solved step by step
Below is one fully worked example plus a short primer so you can see exactly how our AI reasons through a problem.
Example Problem
DEMO5(x - 2) + 3 = 2x + 13
- 1
Expand the bracket
The left side simplifies to 5x − 7.
- 2
Rewrite the equation
- 3
Move variable terms to one side
Subtract 2x from both sides to gather x-terms on the left.
- 4
Move constants to the other side
Add 7 to both sides.
- 5
Divide by the coefficient of x
Check: 5(20/3 − 2) + 3 = 5(14/3) + 3 = 70/3 + 9/3 = 79/3. And 2(20/3) + 13 = 40/3 + 39/3 = 79/3. ✓
Final Answer
How to solve a linear equation — step by step for Class 7 to 12
A linear equation is any equation where the highest power of the variable is 1 — no squared, cubed or root terms. In one variable the goal is simple: isolate x on one side by applying the same inverse operation to both sides (add, subtract, multiply, divide). When brackets appear, expand them first; when fractions appear, multiply through by the LCM to clear them. Multi-variable linear equations like 2x − 5y = 1 have infinitely many solutions on their own and usually come as systems of two equations — solved by substitution (isolate one variable, substitute into the other) or elimination (add or subtract equations to cancel a variable). Linear equations are the gateway to coordinate geometry, inequalities, simultaneous equations and every optimisation problem in SAT, GCSE and CBSE Class 9–10 papers.
Linear equations to practise (one and two variables)
Tap any problem to solve it with full step-by-step working.
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1. 4x - 9 = 3x + 6
One-variableClass 7–8Easy - Solve with AI →2.With fractionsClass 8–9Medium
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3. 2(3x - 4) = 5x + 2
With bracketsClass 8Easy - Solve with AI →
4. 3x + 2y = 12 and x - y = 1
Two-variable systemClass 9–10Medium - Solve with AI →
5. A train travels x km in 3 h and (x + 60) km in 5 h at the same speed. Find x.
Word problemClass 8–9Hard
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Frequently asked questions
How do I solve a linear equation in one variable?+
Move all variable terms to one side and all constants to the other using inverse operations. Expand brackets first and clear fractions by multiplying through by the LCM before isolating x.
How do I solve two linear equations in two variables?+
Two methods: substitution (solve one equation for one variable, substitute into the other) or elimination (multiply equations so one variable cancels when you add or subtract them). Both produce the same answer — pick whichever keeps the numbers cleaner.
What's the difference between a linear equation and a linear inequality?+
A linear equation uses =, a linear inequality uses <, >, ≤ or ≥. Solving is nearly the same, except when you multiply or divide both sides by a negative number — then you must flip the inequality sign. The solution to an inequality is a range of values, not a single point.
Does this solver handle word problems for Class 8 and 9?+
Yes. Paste or photograph the word problem; the AI identifies the unknown, builds the linear equation, solves it, and explains each step in plain English — exactly the format Class 8 and 9 textbooks expect.
Is the linear equation solver free to use?+
SolveGini has a free plan. Guests get 1 solve per day, free accounts get 5 daily solves plus quizzes, flashcards and the study planner — no credit card to start.
Can I use this for GCSE and SAT preparation?+
Yes. Coverage spans GCSE Higher and Foundation tiers (AQA, Edexcel, OCR), SAT Heart of Algebra, and the algebra strands of Common Core Grade 8 through to Algebra II.
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