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hendricks_beginning_algebra_1e_ch1_3

Section 1.3 The Order of Operations, Algebraic Expressions, and Equations 37 b. Translate the phrase: 6 less than a number. �������������������������������������� ���������������������������������������������������������������� The phrase “6 less than a number” is translated as x - 6. The order of this translation is very important. Think of how we find 6 less than 9—that is, 9 - 6 or 3. Note that the expression 6 - x is the translation of “6 less a number” or “the difference of 6 and a number.” The translation is 6 - x. ANSWERS TO STUDENT CHECKS Student Check 1 a. 1000 b. 2.25 c. 216 343 d. -4096 Student Check 2 a. 21 b. 0 c. 1 d. 5 7 e. 6 Student Check 3 a. 5, 8, 11 b. 0, 1 6 , 6 31 , 2 7 c. 16 Student Check 4 a. no b. yes Student Check 5 a. x - 2 b. x + 3 c. 3x + 5 d. x 2 e. x - 4 f. 6x g. 2x - 9 h. 3(x + 1) i. 1 3 x - 5 j. 4x + 1 = 15 k. 2x < 4 Student Check 6 a. $2431.01 b. C = 2πr; 471 m c. d = 0.3x 4 - 18x3 + 308.4x2 + 273.3x + 1096.6;121,469 degrees conferred d. BMR = 66 + 6.23w + 12.7h - 6.8a; 2296 cal 6 SUMMARY OF KEY CONCEPTS 1. An exponent is a way of writing repeated multiplication. The exponent indicates the number of times to repeat the base as a factor. 2. The order of operations is used to simplify numerical expressions. The order is: parentheses (or any grouping), exponents, multiplication/division in order from left to right, and addition/subtraction in order from left to right. 3. To evaluate an algebraic expression, replace the variable with the given value and use the order of operations to simplify the resulting expression. It is helpful to put parentheses around the number being substituted into the expression. 4. An equation is a statement that two expressions are equal. To determine if a number is a solution of an equation, substitute it into the equation. If the resulting statement is true, the number is a solution. If it is not true, the number is not a solution. 5. Be familiar with the common phrases for addition, subtraction, multiplication, division, and equality. Use the phrases to express relationships mathematically. 6. When solving application problems, we must be able to write an appropriate equation that represents the problem and then use the equation to determine values when given specific information. GRAPHING CALCULATOR SKILLS We can use the calculator for simplifying exponential expressions, simplifying numerical expressions, and evaluating algebraic expressions. The most important part of entering a numerical expression is “telling” the calculator where the grouping symbols occur in the problem. We use parentheses to indicate grouping symbols on the calculator. If parentheses are not used correctly, an incorrect order of operations is applied. Example: Use the calculator to find the value of the numerical expressions. 1. a2 3 b 4 MATH 1 ENTER 4 ENTER ( 2 4 3 ) 2. 4 · 5 ÷ 2 + 3 · 8 4 3 5 4 2 + 3 3 8 ENTER


hendricks_beginning_algebra_1e_ch1_3
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