📚 Practice With Worksheets
Strengthen equation-solving skills with additional practice involving inverse operations, variables on both sides, fractions, and isolating variables.
▶️ Learn With Videos
Watch the related lessons to review two-step equations, equations containing fractions and negative numbers, and equations with variables on both sides.
🛠️ How to Use This Tool
Choose a practice topic, select the number types you want to include, and set the number of problems required for the session.
Solve each equation one step at a time. The tool may ask you to choose an operation, perform arithmetic, distribute a factor, combine terms, or classify the number of solutions.
Use the Coach when you need guided support, the Workspace for scratch work, and the Solution tab to review an animated worked solution after attempting the problem.
🧠 Things to Notice
An equation remains balanced only when the same operation is performed on both sides.
When distributing, the factor outside the parentheses must multiply every term inside the parentheses.
A linear equation may have one solution, no solution, or infinitely many solutions depending on what remains after the variable terms are simplified.
📘 Vocabulary
Equation: A mathematical statement showing that two expressions have the same value.
Expression: A combination of numbers, variables, and operations that does not contain an equality sign.
Variable: A letter or symbol used to represent an unknown or changing number.
Coefficient: A numerical factor multiplying a variable, such as \(5\) in \(5x\).
Constant: A number without a variable whose value does not change.
Like Terms: Terms containing the same variable raised to the same power.
Inverse Operations: Operations that undo one another, such as addition and subtraction or multiplication and division.
Distributive Property: A property used to multiply a factor by every term inside parentheses.
Solution: A value that makes an equation true when substituted for the variable.
Equivalent Equations: Equations that have the same solution or solution set.
Linear Equation: An equation in which the variable has an exponent of one and its graph forms a straight line.
📐 Types of Linear Equations
A linear equation has one solution when the variable can be isolated as one specific value.
\(2x+3=11 \quad \Rightarrow \quad x=4\)
A linear equation has no solution when the variable terms cancel and the remaining numerical statement is false.
\(3x+5=3x+9 \quad \Rightarrow \quad 5=9\)
A linear equation has infinitely many solutions when both sides simplify to the same expression and the remaining statement is always true.
\(4(x+2)=4x+8 \quad \Rightarrow \quad 4x+8=4x+8\)
Equations with variables on both sides may result in any of these three outcomes. Simplify both sides carefully before deciding how many solutions the equation has.
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