Section 1.6 Multiplication and Division of Real Numbers 63 Algebraic Expressions Now that we know how to perform operations with signed numbers, we will revisit evaluating algebraic expressions. Recall that we evaluate an algebraic expression by replacing the variable(s) with the given values. Then we use the order of operations to simplify the resulting expression. �� ������������������������ ������������������ Evaluate each expression at the given values. 4a. -b + 1b2 - 4ac 2a , for a = 3, b=-11, c=-20 4b. 3x2 - x + 5, for x = -2, -1, 0, 1, 2 Solutions 4a. -b + 1b2 - 4ac 2a = -(-11) + 1(-11)2 - 4(3)(-20) 2(3) Let a = 3, b = -11, c = -20. = 11 + 1121 - 4(3)(-20) 6 Simplify the opposite of -11 and the exponential expression. Simplify the denominator. = 11 + 1121 - 12(-20) 6 Multiply from left to right inside the square root. = 11 + 1121 + 240 6 Multiply -12 and -20. = 11 + 1361 6 Add the numbers inside the square root. = 11 + 19 6 Simplify the square root. = 30 6 Add the numerators. =5 Divide the numbers. 4b. Make a chart to organize the information. Make the appropriate substitution for the variable. Simplify the expression. x 3x2 - x + 5 -2 3(- 2)2 - (-2) + 5 = 3(4) - (-2) + 5 = 12 + 2 + 5 = 19 Replace x with -2. Simplify the exponent. Multiply. Add or subtract from left to right. -1 3(- 1)2 - (-1) + 5 = 3(1) - (-1) + 5 = 3 + 1 + 5 = 9 Replace x with -1. Simplify the exponent. Multiply. Add or subtract from left to right. 0 3(0)2 - (0) + 5 = 3(0) - (0) + 5 = 0 - 0 + 5 = 5 Replace x with 0. Simplify the exponent. Multiply. Add or subtract from left to right. 1 3(1)2 - (1) + 5 = 3(1) - (1) + 5 = 3 - 1 + 5 = 7 Replace x with 1. Simplify the exponent. Multiply. Add or subtract from left to right. 2 3(2)2 - (2) + 5 = 3(4) - (2) + 5 = 12 - 2 + 5 = 15 Replace x with 2. Simplify the exponent. Multiply. Add or subtract from left to right. Objective 4 ▶ Evaluate algebraic expressions.
hendricks_beginning_algebra_1e_ch1_3
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