Solve equations involving integers

Learning Objectives Define key terms such as equation, variable, and integer. Identify the variable and constant terms in a one-variable equation. Apply inverse operations to isolate the variable in one-step equations. Solve one-step addition and subtraction equations involving integers. Solve one-step multiplication and division equations involving integers. Check their solutions by substituting the value back into the original equation. Ever wonder how detectives solve mysteries? 🕵️‍♀️ Math equations are like puzzles, and you're the detective trying to find the hidden number! In this lesson, you'll learn how to solve equations where a mystery number (a variable) is hidden. This skill helps you find unknown values in everyday situations and builds a strong founda...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal. It always contains an equals sign (=).x + 5 = 12 VariableA symbol, usually a letter (like x, y, or a), that represents an unknown number or value in an equation.In the equation 'x + 5 = 12', 'x' is the variable. IntegerWhole numbers (0, 1, 2, 3, ...) and their opposites (..., -3, -2, -1). Integers do not include fractions or decimals.-5, 0, 10, -100 are all integers. SolutionThe value of the variable that makes the equation true. When you substitute the solution back into the equation, both sides will be equal.For 'x + 5 = 12', the solution is x = 7 because 7 + 5 = 12. Inverse OperationsOperations that undo each other. They are used to 'unravel' an equation...

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 balanced (true). 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 balanced (true). Multiplication Property of Equality If \(a = b\), then \(a \cdot c = b \cdot c\) (where \(c \neq 0\)). You can multiply both sides of an equation by the same non-zero number, and the equation will remain balanced (true). Division Property of Equality If \(a = b\), then \(\frac{a}{c} = \frac{b}{c}\) (where \(c \neq 0\)). You can divide both sides of an equation by the same non-zero number, and the equation will r...