Section 1.3 The Order of Operations, Algebraic Expressions, and Equations 31 3b. x Value of x - 1 x 1 1 - 1 1 = 0 1 = 0 Replace x with 1. 1.5 1.5 - 1 1.5 = 0.5 1.5 = 1 3 Replace x with 1.5. 2 2 - 1 2 = 1 2 Replace x with 2. 3 3 - 1 3 = 2 3 Replace x with 3. 3c. b2 - 4ac = (5)2 - 4(3)(2) Replace b with 5, a with 3, and c with 2. = 25 - 4(3)(2) Simplify the exponential expression. = 25 - 12(2) Multiply 4 and 3. = 25 - 24 Multiply 12 and 2. = 1 Subtract 25 and 24. Student Check 3 Evaluate each expression for the given values. a. Find the value of 3x + 5 for x = 0, 1, and 2. b. Find the value of x - 4 x + 1 for x = 4, 5, 5.2, and 6. c. Find the value of b2 - 4ac when a = 6, b = 8, and c = 2. Solutions of Equations A statement that shows two expressions are equal is an equation. The equals sign “ = ” is used to denote this equality. We will study many different kinds of equations throughout this text. Some examples of equations are 4x + 5 = 9, x2 - x = 6, 1y + 4 = 2y, P = 2l + 2w One of the goals in algebra is to solve an equation. To solve an equation means to find the value(s) of the variable(s) that satisfies the equation, that is, makes the equation true. Each such value is called a solution of an equation. For instance, x =1 is a solution of 4x + 5 = 9: x = 2 is not a solution of 4x + 5 = 9: 4(1) + 5 = 9 4(2) + 5 = 9 4 + 5 = 9 8 + 5 = 9 9 = 9 13 = 9 True False ���������������������� Determining if a Value is a Solution of an Equation Step 1: Replace the variable(s) with the given values. Step 2: Simplify each side of the equation. Step 3: If the resulting equation is true, then the value is a solution. If the resulting equation is false, then the value is not a solution of the equation. Objective 4 ▶ Determine if a value is a solution of an equation.
hendricks_beginning_algebra_1e_ch1_3
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