13) = 4 36 = ) = 5-8 = -3 =3 15) = = -58 = 58 16) = 81-9 = 72 = 72
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- Myron Griffith
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1 Practice Practice Practice 3 ) (-3) + (-6) = -9 ) () + (-5) = -3 3) (-7) + (-) = -8 4) (-3) - (-6) = (-3) + 6 = + 3 5) (+) - (+5) = -3 6) (-7) - (-4) = (-7) + 4 = -3 7) (5)(-4) = - 8) (-3)(-6) = +8 9) (-)() = - ) negative ) positive ) negative 3) (-6) (-4) = +4 4) (-) (5) = -4 5) (3) (-8) = -4 6) (-8) = 64 7) -8 = -64 8) -(8) = -64 9) = ) = + ) B + 8A - 9A - B = B - A ) 4 = 3 48 = 3 LCM = 3 = 48 ) = 5 5 = 3 5 LCM = 3 5 = 3 3) 9 = 3 3 = LCM = 3 3 = 99 4) 35 = = 7 LCM = 5 7 = 8 5) 36 = = 5 5 LCM = = 9 6) 54 = = LCM = = 864 7) -3 + = = = -4 8) = 8 9) (-5) 9 3 = =75 ) 4( + ) - 4 = 4(3) = 38 3) 4 6 = 4 36 = 44 4) 5-3 = 5-8 = -3 =3 5) -3 7 = = -58 = 58 6) 9-3 = 8-9 = 7 = 7 7) ( 3 ) = ( 9) = = = 7 8) = 6 + (3 3) (4 5) = = = - + = 9 ) -4A A - = 8 + 3A + = 3A = - 3A = 9 A = 3 Check: -4(3) (3) - = = 8 + = ) C - C C = 6 4C = 8 = 6 4C = 8 C = Check: to check each equation, substitute the solution for the unknown and simplify. 3) = = 5 4 = 4 = 4) B + B B = (3 4) + 4 8B - 8 = 6 8B = 4 B = 3 5) 4K + + K + K - = 7 7K + - = 49 7K = 49 K = 7 6) 7Q - 4Q Q = - 4Q + = 4Q = Q = 5 8) R + R - 9 = - 7 R - 9 = 3 R = R = 9) C = C C = C + 6 C - 4 = C + 8C = 6 C = ) = = 5 6 = 48 = 8 ) = = = = 5 ) -8 + E E + 5E = E - 3 = E - 3 = 5 6E = 8 E = 3 3) R - 8R R = R + 3 = R = 7 4) Z + 5Z = ( ) 4 Z + = 4 Z + = 5 Z = 48 Z = 4 ) 4C - 3D + 7C = C - 3D - 3) false ) = = -49 = -9 7) 6 + 5A = 3A + 8 5A - 3A = A = A = 6 4) true 5) true ) = + -
2 Practice 4 Practice 5 ) 6(3 + ) = 6(3) + 6() = 8 + = 3 ) 7( ) = 7(3) + 7(4) + 7 () = = 56 3) 5( + ) = ) (4M + Q) = 8M + 4Q 5) 3(A + 3B - + 4A) = 3A + 9B A = 5A + 9B - 6 6) 4( ) = = ) done 8) 4A - 8B = 4(A - B) 9) + 4 = 7(3 + ) ) -5M -N = -5(M + N) ) 5B + 5C = 5 (B + 3C) ) -5 + A = -5( - 4A) 3) done 4) 8B + 6 = 56 8(B + ) = 8(7) B + = 7 B = 5 ) (-, 4) ) II 3) (6, 3) 4) I 5) (, ) 6) I 7) (4, -4) 8) IV 9) (-4, -3) ) III ) on the graph ) II 3) on the graph 5) = = 6 (4-3) = (5) 4-3 = 5 4 = 8 = In #5 and #6, terms were combined to simplify before finding the common factor. ou could also find the common factor first and then simplify. Either method should yield the same answer. 4) I 5) on the graph 6) IV F H 6) = = 8 3( - 4) = 3(6) - 4 = 6 = 7) 5A + = 3 5(A + 4) = 5(6) A + 4 = 6 A = 7) (, ) 8) negative, positive 9) value ) 4 J 8) Q - 4 = 4 (Q - 7) = () Q - 7 = Q = 9
3 Practice 6 ) hours pies - 4 ) on the graph 3) P = 3H - 4) hours arr ) on the graph pies arrangements hours hours Practice 7A and 7B Use after lesson 8 if you have 35 lessons. ) done ) done 3) slope-intercept 4) 5) 4 6) 7) answers will vary: e: = 3 8) C 9) E Practice 9 ) on the graph ) slope = = - 3) y-intercept = - 4) = - - 5) A and B 6) on the graph 7) = ) + = 5 #3 #6 6) A = H + 3 ) D 7) hours problems 6 problems ) B ) A 3) on the graph 9) on the graph ) slope = ) y-intercept = 8) on the graph 9) P = 4H + ) 4 7 hours 4) on the graph 5) on the graph 6) on the graph #3 #5 #6 ) = 3) B and C 4) on the graph 5) = + 6) - = -4 ) on the graph ) Answers will vary. our problem should start with a positive amount. #4 #4 #9
4 Practice Practice Practice ) on the graph ) slope = = 3) y-intercept = 4 4) = ) B and C 6) on the graph ) on the graph ) = -4/5() + b y-intercept = 3/5 3) = -4/5 + 3/5 4) = 8 #5 ) = see graph ) dotted 3) (, ) () + () < 4, < 4 true (, ) () + () < 4, 6 < 4 false 7) = - 8) - = #3 #6 # 4) see graph 5) see graph 9) on the graph ) slope = ) -intercept = ) = 3) C 4) on the graph 5) = ) + = 3 # 5) 4 ( 3) ( ) = 7 (see graph) 6) 4 = 7/() + b 4 = + b; 4 = b 7) = 7/ + 4 8) -7/ + = 4; -7 + = 8; 7 - = - 8 9) (3) = () + b 3 = b = + 3 ) () = -/(-) + b = / + b; b = / = -/ + / ) () = -/3(-) + b = /3 + b; b = /3 = -/3 + /3 ) (3) = 3/4() + b 3 = 3/ + b; b = / = 3/4 + / 3) (-3) = (-) + b -3 = -4 + b; = b = + 4) () = 4() + b = 8 + b; -8 = b = 4-8 5) 3 = 3 = 3 = m (3) = /3() + b 3 = /3 + b; /3 = b = /3 + /3 6) ( 3) ( ) = 3 4 = m () = 3/4() + b 3 = 3/ + b; - / = b = 3/4 - / 6) solid 7) (, ) () -3() - ; - false (-, ) () -3(-) - ; true 8) see graph 9) - = ; = / - ; see graph ) solid ) (, ) () - () ; true (3, ) (3) - (), 3 false ) see graph 3) -4 > - + < /4 - / 4) 3 = 5 /3 + /3 5) -5 < -5-5 > + 3 #4
5 Practice 3 Practice 4 ) on the graph #5 d # a #4 c ) on the graph ) (, ) 3) (-3, -) 4) on the graph 5) on the graph # b ) + (3-5) = = 4 7 = 4, = 6) (, -3) 3) () + = 4 =, = 4) (6, 3) 7) on the graph 8) on the graph 9) (-, ) ) on the graph ) on the graph ) (, 3) #7 e # g # h #8 f 5) - 3(/ ) = -3 - / = -3 -/ = -3, = 6 6) = /(6) = 3 7) (-, 3) 3) on the graph 4) on the graph 5) (-, ) 6) on the graph 7) on the graph 8) (3, 4) #3 j #7 s #4 k #6 r 8) -(-+ ) + = = 5 + = = 9, = 3 9) + 3 = = - ) 5-3(-/3 + 3) = = 7 =, = 3 (3) + 3 = = 9 3 = 3, = (3, )
6 Practice 5 Practice 6 Practice 7 ) (-, -) ) P + N = 65.P +.5N =.5 ) N, N +, N + ) N + (N + ) = (N + ) + 9 ) - + = + ( + = -4) 3 = -3 = - ) (P + N = 65)(-5) = -5P - 5N = -35 (.P +.5N =.5)() = P + 5N = 5-4P = - P = 55 3) N + = N + N =,, 3) - + (-) = - = = - 3) If P = 55 and P + N = 65, then nickels =. 4) + () = () + 9 = 4) Q + N = 7.5Q +.5N = $.85 5) N, N +, N + 6) N + (N + ) + 3(N + ) = 4(N) 4) (-3, 4) 5) + 3 = 6 -(4 + 3 = ) - = 6 = -3 6) (-3) + 3 = = 6 3 = = 4 5) (Q + N = 7)(-5) = -5Q - 5N = - 85 (.5Q +.5N =.85)() = 5Q + 5N = 85 Q = Q = 6) If Q = and Q + N = 7, then nickels = 7 7) N + D = 6.5N +.D =.5 7) N + N + + 3N + 6 = 4N 6N + 8 = 4N N = -8 N = -4-4, -3, - 8) (-4) + (-3)+ 3(-) = 4(-4) = -6-6 = -6 9) N, N +, N + 4 7) (-, -) 8) -5 + = 8 - (3 + = -8) -8 = 6 = - 9) 3(-) + = = -8 = - = - 8) (N + D = 6)(-) = -N - D = -6 (.5N +.D =.5)() = 5N + D = 5-5N = - 55 N = 9) If N = and N + D = 6, then D = 5. ) Q + P = 3.5Q +.P =.46 ) 6(N + ) = (N) ) 6N + = N 4N = - N = -3-3, -, ) 6(-) = (-3) -6 = -6 3) N, N +, N + 4 4) N + (N + ) + (N + 4) = 4(N + ) - 6 ) (Q + P = 3)(-) = -Q - P = - 3 (.5Q +.P =.46)() = 5Q + P = 46 4Q = 6 Q = 9 ) 4 - = + (3 + = -5) 7 = 7 = 4() - = 4 - = - = 8 = -4 (, -4) 5) 3N + 6 = 4N N + 6 = 4N + 4 = N 4, 6, 8 ) If Q = 9 and Q + P = 3, then P = 6) 4 + (6) + (8) = 4(6) = 8
7 Practice 8 Practice 9 Practice ) 96 ) 3 ) + 9 ) ) ± 3) 49 4) 5 ) -3 3) 4) A 3 ) ) - 8 ) ) ± 8 5) 5-6 = 5-4 4) ) ) ) = 7 +4 = 7 6 8) = 9 9) 8-7 = 8 3 ) = 6 = 6 6) = 4-7 7) -4(5) = - 8) (R -3 ) -6 = R 8 9) 7 -() = 7-4 ) A - B + = A B 3 = B 3 5) ) ) ( + )( + 3) = ) 4) 5) ) A +5+4 = A ) R -3+ S -+ = R - S ) R + S 3+4 = R 3 S 7 3) R+S ) A B + C -+ = A B 3 C - 3) B -8+- (-6) = B = 8) ( + )( + 4) = ) ) B 6- = B 4 4) R - 4 = R 8 7) ) P +3-5 = P 5) B 4-3 C + B C -3 = B C 4 B C - = B- C 4- (-) = C 5 9) ( + )( + 5) = ) A B +3 C + = A B 5 C 4 6) Q - R 4 R 3- Q -+ = Q R 4 R Q = R4 R = R 4- = R 3 8)
8 Practice ) ) ) ) + 3) ) 9) Even though we show the drawings, you may not have enough blocks to build some of these ) + 3 5) ) ) ) ) ) ) )
9 Practice ) ( + + ) 6) 3( ) ) 3( ) 6) 3( ) ( + )( + ) ( + 4)( + 9) ) 5( + + ) + + 3) 3( ) ) ( ) ) ( ) ) 4( ) ) ( ) ) ( + + 6) ( + )( + 8) ) ( + + 8) ( + 4)( + 7) ) 4( ) 4( + 3)( + 4) ) ( ) ( + 3)( + 5) ) ( + + 3) ( + 5)( + 6) ) 4( ) 4( + )( + 4)
10 Practice 3 ) ( - )( - 5) Continue to check by multiplying. 7) ( - 3)( - 9) ) ( - 5)( + 7) ) ( - )( - 6) ) ( - 5)( - 6) ) ( - 3)( + 6) ) ( - )( - 7) ) ( - 9)( - ) 4) ( + 4)( - 9) - 7 4) ( - 3)( - 4) ) ( - )( - 8) ) ( - 3)( - ) ) ( - 3)( + 7) 5) ( - 5)( + ) ) ( - 5)( + ) 6) ( - 3)( - 7)
11 Practice 4 Practice 5 ) ) + 5 R ( - ) (5-5) ) ( - 3)( + 3) ) ) ) 5) 6) ( + 4) 3 + -(3 + ) - R ( + 5) - + -( R ( + 3) (4 + 8) -3 Check Continue to check by multiplying. 8) 9) ) ) + 6 R ( + 6) (6 + 36) -8 + R ( + ) - 5 -( + ) R ( ) (-7-8) 9 - -(9 + 76) R ( 3 + ) (6 + 6) (- - ) ) ( - 8)( + 8) ) ( - 6)( + 6) 4) ( - 9)( + 9) 5) ( - )( + ) 6) ( - )( + ) 7) ( - )( + ) 8) ( - )( + ) 9) (A - )(A + ) ) (3-3)(3 + 3) ) (B - 4)(B + 4) ) ( - 5)( + 5) 3) ) ) ) Continue to check by multiplying.
12 Practice 6 ) ( - 4)( + 4) ( - )( + )( + 4) ) (A - B )(A + B ) (A - B)(A + B)(A + B ) 3) 4( - ) 4( - )( + ) 4) ( 3-3 )( ) 5) 4( ) 4( + )( + 3) 6) ( + - 6) ( - )( + 3) 7) B(B + 3B + 6) B(B + )(B + 6) 8) 6( - 3) 9) 4( - 6) 4( - )( + ) ) ( - - ) ( - 4)( + 3) ) 3( ) 3( + 5)( - ) ) 4( 4-6) 4( - 3)( + 3) OR ( - 6)( + 6) ( - 3)( + 3) = 4( - 3)( + 3) 3) A(A + 6A + 5) A(A + 5)(A + ) 4) 6( + - ) 6( + )( - ) 5) ( + 3-9) ( - 3)( + 3) Practice 7 ) ( + 7)( - ) = ) + 7 = = -7 - = = 3) (-7) + 5(-7) - 4 = = = 4) 5(B - 5) = 5(B - 5)(B + 5) = 5) B - 5 = B = 5 7) ( - 3)( - ) = ) - 7 = = 7 B + 5 = B = -5 + = = - () + 5() - 4 = = = 6) 5(5) - 5 = 5(-5) - 5 = 5-5 = 5-5 = = = 8) - 3 = - = = 3 = = 3/ 9) (3/) - 7(3/) + 6 = () - 7() + 6 = (9/4) - / + 6 = = = 4[(9/4) - / + 6] = 4() = = ) ( ) = ( - 7)( + ) = Practice 8 ) foot = inches ) feet in numerator to remain in final answer inches in denominator so they will cancel 3) 8 in ft in 4) 3 feet = yard = 9 ft 5) yards in numerator to remain in final answer feet in denominator so they will cancel 6) 96 ft yd 3 ft 7) 6 ounces = pound = 3 yd 8) ounces in numerator to remain in final answer pounds in denominator so they will cancel 9) 45 lb 6 oz lb = 7 oz ) meter = centimeters ) centimeters in numerator to remain in final answer meters in denominator so they will cancel ) 5 m cm m =,5 cm 3) liter = milliliters 4) liters in numerator to remain in final answer milliliters in denominator so they will cancel 5) 7.8 ml liter ml 6) meters = kilometer =.78 litres 7) kilometers in numerator to remain in final answer meters in denominator so they will cancel 6) ( - 5) ( - 5)( + 5) ) (7) + 8(7) - 54 = = = (-) + 8(-) - 54 = = = 8) 5 m km m =.5 km
13 Practice 9 Practice 3 Practice 3 4 ft ) in ft in ft = 576 in ).4 ) 4 = 3 = 8 5 m ). ft 3).5 ft 4) 3 4 m 5) 3 cm m in ft in ft dm m cm m in ft in ft dm m = 5, cm = 8.8 in = 36 in 3 dm m = 4 dm 3 ). 3). 4).6 5).5 6).9 7).6 ) 3 = 9 3) 5 = 5 3 4) 64 = 4 4 = 6 5) (fractional eponents cancel to ) 6) A /6 km 6) 3 m km m km m km =,,, m 3 8) 8 7) ( 9 ) /3 = ft 7) 3 yd 3 ft yd 3 ft yd 3 ft = =.5 yd 3 9) in.5 cm in = 5 cm 4 8) 8 = = 7 8) 3456 in3 ft in ft in ft in = = ft 3 ) 4 g oz 8 g = 4 8 = or.5 oz 9) (9) / = 3 ) (4) / = 5 = 9) 46,656 in 3 yd 36 in yd 36 in yd 36 in = 46,656 46,656 = yd 3 ) yd.9 m yd = 8.9 m ) (8) /3 = 5 cm ) 3 m cm m cm m 5 = =.5 m cm,, 3 ) 44 kg. lb kg = 96.8 lb ) ( ) / = 5 5 cm m ) m 5 = =.5 m cm cm, 3) 4. mi.6 km mi = 6.56 km 3) ( ) 5 = 5 ) 43,56 ft 3) 4 ft 4 ft 8 ft = 8 ft 3 4) 7 ft 3 4 l 4).6 qt l 5) 7 oz 8 g oz = 4.4 qt = 96 g 4) ( 6 ) 3/4 = ( 8 ) 3/4 = 6 5) (A 5/4 ) /3 = 5/6 6) (M 9/6 ) /3 = M 5) 9 ft 6) 5 cm.4 in cm = in
14 Practice 3 Practice 33 ) 5 ) ) ) 3 3 = ) (49) + (7) + 5() = = 7 4) ).68-6) -7 7) ( 5 )(5.9 9 ) ( 5.9)( 5 9 ) =.58 4 = using significant digits ) 5 = ) (5) + (5) + () = = 77 8) ( )(. 7 ) (6.55.)( 5 7 ) = = using significant digits 9) (4.5 4 )(8. 5 ) (4.5 8.)( 4 5 ) = = using significant digits ) (6-4 )(3 9 ) (6 3)( -4 9 ) = 8 5 = using significant digits ) (4. -4 )(6 4 ) (4. 6)( -4 4 ) = 5. =.5 3 using significant digits ) ( )(3.7-4 ) ( )( - -4 ) = = using significant digits 3) (. 5 ) (9 9 ) (. 9)( 5 9 ) = = using significant digits 4) (5.8 6 ) (.76 5 ) (5.8.76)( 6 5 ) = 3 3. using significant digits 5) (.75 - ) (.5-3 ) (.75.5)( - -3 ) =. same using significant digits 3) 4 3 = ) 6 = ) 4 5 = ) 5 4 = ) (7) + (9) + (3) + () = = 5 ) (5) + 4(5) + 4(5) + () = = 37 ) 5 () + () + () 5(44) + () + () = = 84 ) (3) + 7 (3) + 3 (3) (69) + 7(3) + 3() = = 953
15 Practice 34 ( + ) = 4 + = ± =, = -3 ( + ) = 4 + = ± =, = -3 ) 5, -5 ) 5, -5 3) (, ) 4) 5 5), -3 6), -3 7) (-, -) 8) = 8 = 4 = ± = = = ± 4 = 8 = = ± 5 = = 4 = ± 9), - 3), - ) ellipse ), - 3), - 4) ellipse ( - 4) = 4-4 = ± = 6, = ( + ) = 4 + = ± =, = -4 5) on the graph 6) on the graph
16 Practice 35 ) ) ) /3-4 -6/3-4/3 - -4/3 4) ) 6) /4 - /
1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =
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