Linear Equation Solver

Understanding Linear Equations

A linear equation is a mathematical statement that expresses the equality of two algebraic expressions containing one or more variables raised to the first power. The most common form of a single-variable linear equation is $ax + b = 0$, where $a$ and $b$ are constants, and $x$ is the variable to solve.

How to Solve Linear Equations Step by Step

Solving a linear equation involves finding the value of the variable that makes the equation true. Here are the core steps to solve any linear equation:

1. Simplify Both Sides: Distribute any multiplication across parentheses, combine like terms, and remove any fractions by multiplying both sides by the denominator.
2. Isolate the Variable: Move all terms containing the variable (e.g., $x$) to one side of the equation (usually the left side) and all constant numbers to the opposite side.
3. Combine Like Terms: Combine the variable coefficients and simplify the constants to obtain a simplified expression of the form $Ax = B$.
4. Solve: Divide both sides by the variable's coefficient ($A$) to find the final value: $$x = \frac{B}{A}$$

Example Calculations

Let us solve the equation $3x + 5 = 20$:

• Subtract $5$ from both sides: $3x = 15$
• Divide both sides by $3$: $x = 5$