Solve linear equations with step-by-step working and verification
Solving linear equations is one of the most important skills in GCSE maths, appearing across all exam boards including AQA, Edexcel, and OCR. From simple one-step equations to those with unknowns on both sides, algebraic manipulation forms the backbone of the Algebra strand in the UK National Curriculum. Our algebra solver calculator handles three common equation types: ax + b = c (unknown on one side), ax + b = cx + d (unknowns on both sides), and rearranging y = mx + c to find x. Each solution includes full step-by-step working and a verification check, mirroring the approach expected in GCSE exams where showing your working is essential for full marks. This tool is designed for students revising linear equations for GCSE maths, teachers demonstrating algebraic techniques in class, and anyone who needs to solve or check a linear equation quickly. The step-by-step display helps you understand the method so you can apply it independently in exams and beyond.
To solve a linear equation: 1. Select the equation type from the dropdown menu. Choose "ax + b = c" for equations with x on one side only, "ax + b = cx + d" for equations with x on both sides, or "y = mx + c (solve for x)" to rearrange the straight line equation. 2. Enter the values for each coefficient. For "ax + b = c", enter a (the coefficient of x), b (the constant), and c (the right-hand side). For example, for 2x + 3 = 7, enter a = 2, b = 3, c = 7. 3. For "ax + b = cx + d", also enter d. For example, for 3x + 5 = x + 11, enter a = 3, b = 5, c = 1, d = 11. 4. For "y = mx + c", enter a as the value of y, c as the slope m, and b as the intercept c. For example, to solve 5 = 2x + 1, enter a = 5, b = 1, c = 2. 5. Review the results: the solution for x, the formatted equation, step-by-step working, and verification (substituting x back in to confirm the answer is correct).
Linear equations are solved by isolating the unknown variable x using inverse operations. Type 1: ax + b = c Step 1: Subtract b from both sides: ax = c - b Step 2: Divide both sides by a: x = (c - b) / a Example: 2x + 3 = 7. Subtract 3: 2x = 4. Divide by 2: x = 2. Verification: 2(2) + 3 = 4 + 3 = 7. Correct. Type 2: ax + b = cx + d Step 1: Subtract cx from both sides: (a - c)x + b = d Step 2: Subtract b from both sides: (a - c)x = d - b Step 3: Divide both sides by (a - c): x = (d - b) / (a - c) Example: 3x + 5 = x + 11. Subtract x: 2x + 5 = 11. Subtract 5: 2x = 6. Divide by 2: x = 3. Verification: Left side = 3(3) + 5 = 14. Right side = 3 + 11 = 14. Correct. Special cases: If a = c (same coefficient of x on both sides), either there is no solution (when b does not equal d, the lines are parallel) or there are infinite solutions (when b = d, the equations are identical). Type 3: y = mx + c (rearrange for x) Step 1: Subtract c from both sides: y - c = mx Step 2: Divide both sides by m: x = (y - c) / m Example: 5 = 2x + 1. Subtract 1: 4 = 2x. Divide by 2: x = 2. In GCSE maths exams, you must show each step of your working to earn method marks. Even if you make an arithmetic error, correct method steps will earn partial credit. Always verify your answer by substituting back into the original equation.