📚 Practice With Worksheets
Continue practicing with two-step equations, equations with variables on both sides, and equations that have fractional coefficients.
▶️ Learn With Videos
Review strategies for equations with variables on both sides, fractions and negative values, and division involving fractions.
🛠️ How to Use This Tool
Use the Equation Balancer to practice maintaining equivalence while solving equations. The main goal is to keep both sides balanced as you work toward isolating the variable.
Choose one or more problem modes: Whole Numbers, Fractions, or Decimals. When more than one mode is selected, the app can mix those number types. Turn on Negatives to allow positive and negative values within the selected modes.
For each equation, choose Add, Subtract, Multiply, or Divide, enter the number or x-term, and apply the move to both sides. The Equation Trail records your moves so you can review how the equation changed while remaining equivalent.
After two balancing moves—or as soon as the equation is solved—you may open Show Possible Path to study one valid algebraic solution written with mathematical notation.
🧠 Things to Notice
Applying the same operation to both sides preserves the equality, even when the equation looks different after the move.
Inverse operations can create zero pairs, remove constants, or turn a coefficient into 1 so the variable becomes isolated.
There may be more than one valid sequence of balancing moves. A correct path keeps every equation equivalent and ends with the same solution.
📘 Vocabulary
Equation: A mathematical sentence showing that two expressions are equal.
Variable: A letter or symbol that represents an unknown number.
Coefficient: The number multiplied by a variable. In \(3x\), the coefficient is \(3\).
Constant: A number without a variable. In \(2x + 5 = 17\), the constants are \(5\) and \(17\).
Isolate: To get the variable by itself on one side of the equation.
Inverse Operations: Operations that undo each other, such as addition and subtraction or multiplication and division.
Zero Pair: A pair of numbers that add to zero, such as \(+5\) and \(-5\).
Identity Property of Multiplication: Multiplying or dividing to make a coefficient of \(1\), so the variable can stand alone.
Balanced Equation: An equation that stays equal because the same operation is applied to both sides.
📐 Properties of Equality
Adding or subtracting the same value on both sides produces an equivalent equation.
\(a=b \Longrightarrow a+c=b+c \quad \text{and} \quad a-c=b-c\)
Multiplying or dividing both sides by the same nonzero value also preserves equality.
\(a=b \Longrightarrow ac=bc \quad \text{and} \quad \dfrac{a}{c}=\dfrac{b}{c},\; c\ne0\)
The equation may change form after each move, but its solution set remains unchanged when the properties of equality are used correctly.
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