Linear Equations (One Variable)

Solve linear equations of the form $ax + b = c$. Learn to perform inverse arithmetic operations symmetrically to isolate variables while keeping the equation balanced.

Algebra Principles

Isolating Variables

Solving a linear equation means finding the value of the unknown variable that makes the equation true. To do this, we isolate the variable by performing **inverse operations** on both sides of the equation.

Golden Rules of Algebra


  • Keep It Balanced: Whatever operations you perform on the left side of the equation (addition, subtraction, multiplication, division), you must also perform on the right side.
  • Undo Constants First: Use addition or subtraction to move constant numbers away from the variable term.
  • Undo Coefficients Last: Use multiplication or division to clear the coefficient multiplying the variable, leaving just $1x$.

Solving Example

Equation: $3x + 4 = 19$

Step 1: Undo constant addition (+4)
Subtract 4 from both sides:
$3x + 4 - 4 = 19 - 4 \implies 3x = 15$

Step 2: Undo coefficient multiplication (×3)
Divide both sides by 3:
$\frac{3x}{3} = \frac{15}{3} \implies x = 5$