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How linear equations are solved
A linear equation is an algebraic equation of the first degree. The general form is \(ax + b = cx + d\). To solve for \(x\):
- **Group like terms:** Move the variable terms to the left side and constant terms to the right side of the equals sign: \((a - c)x = d - b\).
- **Isolate the variable:** Divide both sides by the combined coefficient: \(x = \frac{d - b}{a - c}\).
- **Undefined Cases:** If \(a = c\) and \(b = d\), there are infinite solutions. If \(a = c\) but \(b \neq d\), there is no solution (contradiction).