Algebra 1 Basic

Linear Equation Solver

Solve any linear equation in one variable — fractions, decimals, parentheses, variables on both sides.

Live Calculator · Step-by-Step · Algebra 1
Enter Equation
Type the full equation with an equals sign. Use / for fractions, * or juxtaposition for multiplication.
Examples
Solution
Enter an equation above and press Solve to see the solution, solution type, and a verification check.
Solution
Verification Check
Step-by-Step Solution
Number Line
Types of Linear Equations
ax + b = cx + d

One Solution: When you move all x terms to one side, the coefficient of x is non-zero. You can divide to isolate x and get a single numeric answer. This is the most common case.

No Solution: When all x terms cancel and the remaining constants are not equal (e.g. 3 = 7). The equation is a contradiction — no value of x can ever make it true.

Infinite Solutions: When all x terms and all constants cancel, leaving 0 = 0 (always true). Every real number satisfies the equation — the two sides are identical expressions.

The key insight: collect x terms on one side, constant terms on the other, then divide by the coefficient of x.
Checking Your Answer
Substitute x back into the original equation

After solving, plug your answer back into the original equation and simplify both sides. If both sides equal the same number, your answer is correct.

Example: For 3x + 7 = 2x − 5 with x = −12:

LHS: 3(−12) + 7 = −36 + 7 = −29

RHS: 2(−12) − 5 = −24 − 5 = −29

−29 = −29 ✓

  • Always check with the original equation, not a simplified version.
  • For fractions, substitute and simplify carefully.
  • For no solution, show that the equation is a false statement.
  • For infinite solutions, show both sides are always identical.

Still getting stuck on linear equations?

One-on-one Algebra tutoring builds the confidence to tackle any equation — we work through your actual homework and tests so the strategies become second nature.

Book a Free Consultation →