Solve equations using properties

Learning Objectives Define an equation, variable, and solution. Identify inverse operations for addition, subtraction, multiplication, and division. Apply the Addition and Subtraction Properties of Equality to solve one-step equations. Apply the Multiplication and Division Properties of Equality to solve one-step equations. Solve two-step linear equations using a combination of properties of equality. Check their solutions by substituting the value back into the original equation. Ever wonder how detectives solve mysteries? 🕵️‍♀️ They use clues to find the unknown! In math, we'll be detectives solving for unknown numbers in equations. In this lesson, you'll learn how to solve equations by using special rules called 'properties of equality'. This skill is...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal, usually containing an equals sign (=).$x + 7 = 15$ VariableA symbol, usually a letter (like x, y, or a), that represents an unknown number or value.In $3x = 12$, 'x' is the variable. SolutionThe value(s) of the variable that make the equation true when substituted back into the equation.For $x + 7 = 15$, the solution is $x = 8$ because $8 + 7 = 15$. Inverse OperationsOperations that undo each other. For example, addition is the inverse of subtraction, and multiplication is the inverse of division.To undo adding 5, you subtract 5. To undo multiplying by 3, you divide by 3. Isolate the VariableThe goal of solving an equation: to get the variable by itself on one side of the equals sign.In...

Addition Property of Equality If $a = b$, then $a + c = b + c$. You can add the same number to both sides of an equation, and the equation will remain true. This is used to undo subtraction. Subtraction Property of Equality If $a = b$, then $a - c = b - c$. You can subtract the same number from both sides of an equation, and the equation will remain true. This is used to undo addition. Multiplication Property of Equality If $a = b$, then $ac = bc$. You can multiply both sides of an equation by the same non-zero number, and the equation will remain true. This is used to undo division. Division Property of Equality If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. You can divide both sides of an equation by the same non-zero number, and the equation...