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hendricks_intermediate_algebra_1e_ch1_3

Section 1.2 Operations with Real Numbers and Algebraic Expressions 23 4d. 2 - 59 - 3(4 - 6) ÷ 3 · 8 = 2 - 59 - 3(-2) ÷ 3 · 8 Simplify within the innermost grouping. = 2 - 59 + 6 ÷ 3 · 8 Multiply -3 and -2. = 2 - 515 ÷ 3 · 8 Add 9 and 6. = 2 - 75 ÷ 3 · 8 Multiply -5 and 15. = 2 - 25 · 8 Divide -75 by 3. = 2 - 200 Multiply -25 by 8. = -198 Subtract. 4e. The fraction bar is a grouping symbol, so we apply the order of operations in the numerator and the denominator 2 - 3u5 - 9u2 -4 - 14 + 12 2 - 3u-4u2 = -4 - 116 = 2 - 3(4)2 -4 - 4 = 2 - 3(16) -8 2 48 = - -8 -46 = -8 = 23 4 Simplify within the absolute value symbol and simplify within the square root symbol. Simplify the absolute value of -4 and simplify the square root of 16. Simplify the square of 4 and subtract the numbers in the denominator. Multiply 3 and 16. Subtract the numbers in the numerator. Simplify the fraction. Student Check 4 Use the order of operations to simplify each expression. a. 6 - (-2) -3 - 1 b. 2(-1)2 - 8(-1) + 5 c. #1 - (-7)2 + (-4 - 2)2 d. 7 + 23(9 - 8) - (5 + 2)4 - 4 · 6 ÷ 8 e. 3 - 612 + 7 -3u1 - 6u2 Evaluating Algebraic Expressions Thus far we have examined numerical expressions; we will now turn our attention to algebraic expressions. Algebraic expressions are expressions joining numbers and letters by mathematical operations. The letters are called variables and represent some unknown number. Examples of variables are x, y, z, a, and b. Examples of algebraic expressions are 2x 4y - 5 b2 - 4ac y2 - y1 x2 - x1 Algebraic expressions are fundamental to the study of algebra. Algebraic expressions are used in formulas, mathematical models, and equations. Our ability to work with these expressions enables us to manipulate the expressions to obtain what is needed. Objective 5 ▶ Evaluate algebraic expressions. The numbers 1 and 2 are called subscripts. They are used to differentiate two different, but related, variables.


hendricks_intermediate_algebra_1e_ch1_3
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