Complete addition and subtraction equations with integers

Learning Objectives Define and identify integers and equations. Solve one-step addition equations involving integers. Solve one-step subtraction equations involving integers. Apply inverse operations to isolate a variable in an equation. Verify solutions by substituting them back into the original equation. Translate simple word problems into addition or subtraction equations with integers and solve them. Ever wonder how much money you have left after spending some and earning some, or how a submarine's depth changes? 💰 Understanding equations with integers helps us track these changes! In this lesson, you'll learn how to find missing numbers in addition and subtraction problems that involve positive and negative whole numbers. We'll use special rules to &#0...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples include -3, 0, 5.The set of integers includes {... -3, -2, -1, 0, 1, 2, 3 ...}. EquationA mathematical statement that shows two expressions are equal, separated by an equals sign (=).$x + 7 = 10$ is an equation. VariableA symbol, usually a letter, that represents an unknown number or value in an equation.In the equation $y - 4 = -1$, 'y' is the variable. Inverse OperationsOperations that 'undo' each other. Addition is the inverse of subtraction, and subtraction is the inverse of addition.To undo adding 5, you subtract 5. To undo subtracting 3, you add 3. Solution (of an equation)The value of the variable that makes the equation a true statement.For...

Addition Property of Equality If you add the same number to both sides of an equation, the equation remains balanced (true). $a = b \implies a + c = b + c$ Use this rule to isolate a variable when a number is being subtracted from it. Add the number to both sides. Subtraction Property of Equality If you subtract the same number from both sides of an equation, the equation remains balanced (true). $a = b \implies a - c = b - c$ Use this rule to isolate a variable when a number is being added to it. Subtract the number from both sides. Rule for Subtracting Integers Subtracting an integer is the same as adding its additive inverse (its opposite). $a - b = a + (-b)$ This rule helps simplify equations that involve subtracting negative numbers, turning them into addition p...