Algebra: Linear Equations

Concept Explanation

A linear equation in one variable has the form ax + b = c, where a ≠ 0. Solving means finding the value of x that makes the equation true.

Method

• Transpose constants to one side and the variable term to the other.
• Divide both sides by the coefficient of x.
• Check by substituting the value back.

Key Form

ax + b = c ⇒ x = (c − b) / a

Example

Solve 3x + 5 = 20. Subtract 5: 3x = 15. Divide by 3: x = 5.

Common Trap

When dividing by a negative coefficient, the inequality sign flips — but in equations, signs cancel correctly if you follow the same operation on both sides.