2.1.1 Addition and Subtraction Equations
Key Objectives • Solve equations by addition. • Solve equations by subtraction. • Write equations. Key Terms • An equation is a mathematical statement that two expressions are equal. • Inverse operations are operations that undo each other: addition and subtraction, or multiplication and division. • Isolate the variable means to get a variable alone on one side of an equation or inequality in order to solve the equation or the inequality. • A solution of an equation is a value of the variable that makes the equation true. • To solve is to find an answer or a solution. Solving an equation means finding its solution, which is the value (or values) of the variable that make the equation a true statement. An equation is like a balanced scale. The expression to the left of the equal sign is the same as, or equivalent to, the expression on the right side of the equal sign. To maintain its balance, any operation performed on the expression on one side of the equation must also be performed on the expression on the other side of the equation. This is often referred to as operating on “both sides” of the equation. The process of solving an equation involves performing operations to both sides of the equation with the goal of isolating the variable on one side of the equation. The variable is isolated when a single instance of it appears on either side of the equation. For example, in the equation x = 4, the variable x is isolated on the left side of the equation. In the examples below, one-step equations are solved by using inverse operations, which “undo” operations on the variable. Addition and subtraction are examples of inverse operations. Example 1 Solving an Equation by Addition Prof. Burger demonstrates the process for solving a one-step subtraction equation in the following Example. The given equation x − 3 = 15 is a one-step subtraction equation because there is only one operation performed on the variable, and that operation is subtraction.
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