Reading to Learn Mathematics

Transcription

1 Reading to Learn Mathematics Vocabulary Builder This is an alphabetical list of the key vocabulary terms you will learn in Chapter. As you study the chapter, complete each term s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter. Vocabulary Term absolute value Found on Page Definition/Description/Example Vocabulary Builder algebraic expression Associative Property uh SOH shee uh tihv Commutative Property kuh MYOO tuh tihv compound inequality Distributive Property dih STRIH byuh tihv empty set Identity Property intersection Inverse Property (continued on the next page) Glencoe/McGraw-Hill vii Glencoe Algebra

2 Reading to Learn Mathematics Vocabulary Builder (continued) Vocabulary Term irrational numbers Found on Page Definition/Description/Example open sentence rational numbers Reflexive Property set-builder notation Substitution Property Symmetric Property suh MEH trihk Transitive Property Trichotomy Property try KAH tuh mee union Glencoe/McGraw-Hill viii Glencoe Algebra

3 - Expressions and Formulas Find the value of each expression (3 8) (4) ( ) 7 6(7 5) 4 5. [ 9 0(3)] (68 7) [3(5) 8 ]5 85 Lesson - Evaluate each expression if r, s, t, v 0, and w. 9. 6r s 0 0. st 4rs 84. w(s r). s r 6v 3. (4s) s r wt 3 3v t 5s t 5. (3r w) rv 7. w[t (t r)] s w r 9. 9r (s )t s v. TEMPERATURE The formula K C 73 gives the temperature in kelvins (K) for a given temperature in degrees Celsius. What is the temperature in kelvins when the temperature is 55 degrees Celsius? 38 K 5. TEMPERATURE The formula C (F ) gives the temperature in degrees Celsius 9 for a given temperature in degrees Fahrenheit. What is the temperature in degrees Celsius when the temperature is 68 degrees Fahrenheit? 0 C Glencoe/McGraw-Hill 3 Glencoe Algebra

4 - Properties of Real Numbers Name the sets of numbers to which each number belongs.. 34 N, W, Z, Q, R. 55 Z, Q, R Q, R 4. N, W, Z, Q, R 5. 9 Z, Q, R I, R Name the property illustrated by each equation x x 8. 3a 0 a Comm. ( ) Add. Iden. 9. (r w) r w 0. r (3r 4r) (r r) 4r Distributive Assoc. ( ) 5y. 5y. 5x() 5x Mult. Inv. Mult. Iden. Lesson [5(0.5)] [0.6(5)] (0b b) 7b (b 0b) 7b Assoc. ( ) Comm. ( ) Name the additive inverse and multiplicative inverse for each number , , , , Simplify each expression. 9. 3x 5 x 5x 0. x y z y x z 0. (3g h) 5g 0h g h. a a 4a a a a 3. 3(m z) 5(m z) 3m 8z 4. x y (5x y z) 3x z 5. 6( v) 4(v ) 8 v 6. (5d ) (8 0d) 0d Glencoe/McGraw-Hill 9 Glencoe Algebra

5 -3 Solving Equations Write an algebraic expression to represent each verbal expression.. 4 times a number, increased by 7. 8 less than 5 times a number 4n 7 5n times the sum of a number and 5 4. the product of 3 and a number, divided by 9 6(n 5) 3n times the difference of 4 and a number 3(4 n) 6. the product of and the square of a number n Write a verbal expression to represent each equation Sample answers are given. 7. n x 5 The difference of a number The sum of 8 and 3 times a and 8 is 6. number is b b y 0. y 3 Three added to the square of a number is the number. A number divided by 3 is the difference of and twice the number. Name the property illustrated by each statement.. If a 0.5b, and 0.5b 0, then a 0.. If d f, then d f. Transitive ( ) Subtraction ( ) 3. If 7x 4, then 4 7x. 4. If (8 7)r 0, then 5r 0. Symmetric ( ) Substitution ( ) Lesson -3 Solve each equation. Check your solution. 5. 4m x 4 5x 7. 3t t b 7 5 b 9. 5x x v a 5. a 5..n 0.8n 5 4n 5 5 Solve each equation or formula for the specified variable. I 3. I prt, for p p 4. y x, for x x 4y 48 rt 4 x y 5. A, for y y A x 6. A r A r rh, for h h r Glencoe/McGraw-Hill 5 Glencoe Algebra

6 -4 Solving Absolute Value Equations Evaluate each expression if w 0.4, x, y 3, and z 0.. 5w. 9y y z z z x y y 5x z x y w w.6. 3x y w 7 Solve each equation. Check your solutions. 3. y { 5, } 4. 5a 0 {, } k 6, 6. g 6 0 { 3} 7. 0 c { 9, } 8. x x 9 { 3, 3} 9. p w {, }. 7x x 8 { 4, 4}. 4 7 y {4, 0} Lesson n, 4. 8d 4d 5 {, } a 5, 6. k 0 9 Glencoe/McGraw-Hill Glencoe Algebra

7 -5 Solving Inequalities Solve each inequality. Describe the solution set using set-builder or interval notation. Then, graph the solution set on a number line. z 4. {z z 8} or (, 8]. 3a 7 6 {a a } or (, 3] q 4 {q q 4} or (4, ) 4. 0 s 7s {s s } or (, ) x 9 {x x 3} or [ 3, ) 6. 4b 9 7 {b b 4} or (, 4] z 9 5z {z z } or (3, ) 8. 7f 9 f {f f } or (, ) s 8 5s {s s } or [, ) 0. 7t (t 4) 5 7 t t or,. 0.7m 0.3m m 4 {m m 4}. 4(5x 7) x x or or (, 4] 3 4 3, y {y y.4} 4. 4x 9 x {x x 5} or (5, ) or (3.4, ) Define a variable and write an inequality for each problem. Then solve. 5. Nineteen more than a number is less than 4. n 9 4; n 3 6. The difference of three times a number and 6 is at least 8. 3n 6 8; n 8 7. One half of a number is more than 6 less than the same number. n n 6; n 8. Five less than the product of 6 and a number is no more than twice that same number. 6n 5 n; n 5 4 Lesson -5 Glencoe/McGraw-Hill 7 Glencoe Algebra

8 -6 Solving Compound and Absolute Value Inequalities Write an absolute value inequality for each of the following. Then graph the solution set on a number line.. all numbers greater than or equal to. all numbers less than 5 and greater or less than or equal to n than 5 n Lesson all numbers less than or greater 4. all numbers between 6 and 6 n 6 than n Write an absolute value inequality for each graph. 5. n 6. n 4 7. n 8. n.5 Solve each inequality. Graph the solution set on a number line. 9. c 5 or c 0 {c c 0. 4y {y y } or c 0}. 0 5x 5 {x x }. 4a 8 or a 3 {a a or a 3} 3. 8 x 3 {x x 7} 4. w 4 0 or w 6 all real numbers t {t t 3 or t } 6. 6x {x x } 7. 7r 4 {r r or r } 8. p 9. n 5 7 {n n } 0. h 5 {h h 6 or h 4} Glencoe/McGraw-Hill 33 Glencoe Algebra