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.
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.
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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 ⇒ 3x = 15
Step 2: Undo coefficient multiplication (×3)
Divide both sides by 3:
3x / 3 = 15 / 3 ⇒ x = 5
Balance Scale Weight Simulator
Clear constants and divide variables on the balance scale. Adjust coefficients a, b, c using sliders to set the initial equation, then click buttons below to step through inverse operations.