Linear Equation Solver

A linear equation in one variable has the form $ax + b = 0$, where $a$ and $b$ are constants and $a \neq 0$. The solution is $x = -\frac{b}{a}$. The graph of $y = ax + b$ is a straight line, and the solution is where it crosses the x-axis.

Yes. If simplifying leads to a contradiction like $3 = 5$ (where the variable cancels out), the equation is inconsistent and has no solution. This happens when both sides have the same variable term but different constants.

Yes. If simplifying leads to a true identity like $0 = 0$ (where everything cancels), the equation is true for all values of $x$. This means both sides are identical expressions.

Multiply every term by the least common denominator (LCD) to clear all fractions first. For example, in $\frac{x}{2} + \frac{x}{3} = 5$, multiply through by 6 to get $3x + 2x = 30$, then solve $5x = 30$ to find $x = 6$.

Follow these steps: (1) distribute to remove parentheses, (2) combine like terms on each side, (3) move variable terms to one side using addition or subtraction, (4) move constant terms to the other side, (5) divide by the coefficient of $x$.