379 Appendix ASection A.1 1.( ) ( ) ( ) ( ) 2, 4 , 3,1 , 4, 3 , and4, 2 A B C D 44 44yx(4, 2)(4, 3)(2, 4)(3, 1) Section A.2 1. 25 is a real number. 2. 40 is undefined. Not a real number. 3.9 3i =is imaginary. Not a real number. 4.3 is a real number. 5.9 3 =is a real number. 6.4.21529is a real number. 7. 005=is a real number. 8.7is a real number. Section A.3 1.3 3 =2.4.69 4.69 =3.0 0 =4. =Section A.4 1.a.( ) 3 7 21 = b.( ) 9 4 36 =c.( ) 5 6 30 = d.( ) 8 2 16 =e.( ) ( )( ) 4 1 4 4 = =f.( ) ( ) ( )( ) ( )( )( )( )9 1 91 1 99 = = = g.( )8 81 42 2 = = h. 6 632 2= = i.( )( )( )12 1214 4121 143 = = = j.( )9 91 33 3 = = 2.a.( ) 3 5 8 + = b.( ) 9 3 6 + =c.( ) 2 8 6 + = d.7 3 4 + = e.( ) 1 8 9 + = f.17 15 2 + = g.( ) 4 6 10 + = h.( ) 2 3 5 + = Appendix ASSM: Intermediate Algebra 380 3.a.( ) 3 7 3 7 4 = + = b.( ) 2 8 2 810 = += c,( ) ( ) ( )5 3 5 35 38 = += += d.( ) ( ) ( )9 4 9 49 45 = += += e.( ) 3 8 3 85 = += f. ( ) 2 4 2 46 = += g.( ) ( ) ( )1 1 1 11 12 = += += h.( ) ( ) ( )10 6 10 610 64 = += += Section A.5 1.y mx b = + Equation 2. 38 x Expression 3.2 5 1 x + Expression 4. 23 5 4 8 x x + =Equation Section A.6 1.( ) ( ) 2 4 2 2 42 8x xx+ = += + 2.( ) ( ) 3 5 3 3 53 15x xx = = 3.( ) ( ) 5 6 5 5 65 30x xx + = = 4.( ) ( ) 3 8 3 3 83 24x xx = = + 5.( ) ( ) ( ) 4 3 2 4 3 4 212 8x xx = = 6.( ) ( ) ( ) 5 2 7 5 2 5 710 35x xx+ = += + 7.( )( ) ( ) 3 4 4 3 44 12x xx = = 8.( )( ) ( ) 4 7 7 4 77 28x xx = = + 9.( ) ( ) 2.8 4.1 2.8 2.8 4.12.8 11.48x xx+ = += + 10.( ) ( ) 5.2 3.9 5.2 5.2 3.95.2 20.28x xx + = = Section A.7 1.( ) 4 3 4 37x x xx+ = += 2.( ) 7 5 7 52x x xx = = 3. ( ) ( )2 2 2 2223 2 7 4 3 7 2 43 7 2 410 6x x x x x x x xx xx x+ + + = + + += + + += + 4. ( ) ( ) ( )2 2226 3 9 2 5 36 3 9 2 5 33 11 2x x x xx xx x + + + = + + + = + + 5. ( ) ( ) ( )2 22 2228 4 1 58 4 1 58 1 4 1 1 57 3 4x x x xx x x xx xx x + + = + + = + + + = SSM: Intermediate AlgebraAppendix A 381 6. ( ) ( )2 22 22221 11 11 1 (1 1) 1 12 0 02x x x xx x x xx xx xx+ + + = + + + = + + + = + += 7.( )( ) ( )4 1 2 3 4 4 2 34 2 4 34 2 4 36 1x x x xx xxx + + = + += + += + + += 8.( )( ) ( ) ( )2 22 22 2225 2 3 4 75 10 3 4 73 7 5 10 43 7 5 1 10 44 6 14x x x xx x x xx x x xx xx x + + = + + + = + += + + += + 9. ( ) ( ) ( )2 22 2225.4 2.1 3.9 1.3 4.4 1.65.4 1.3 2.1 4.4 3.9 1.65.4 1.3 2.1 4.4 3.9 1.64.1 2.3 5.5x x x xx x x xx xx x + + += + + += + + + += + + 10.( ) ( )( ) ( )2.4 6.2 3.9 5.12.4 14.88 3.9 19.892.4 3.9 14.88 19.892.4 3.9 14.88 19.891.5 34.77x xx xx xxx + += + + += + + += + + += + Section A.8 1.( ) 3 5 2 3 1013+ = += 2.( ) 2 8 4 16 412 = = 3.2 10 5 2 24+ = += 4.14 7 1 2 11 = = 5.( ) ( ) ( ) ( ) 2 3 1 4 2 2 2 4 24 812 + = += += 6.20 5 2 4 4 2 48 44 = = = 7.( )( ) ( )( ) 9 5 3 2 5 2 4 5 5 220 5 24 26 + + = += += += 8.( ) ( )( )4 8 3 2 1 4 8 6 14 2 12 11 = = = = 9.( ) ( )24 3 4 936== 10.( ) ( )35 2 5 840== 11.( )( )( )223 1 31 99 = = = 12.( ) ( )( )23 3 39 = = 13. 25 4 3 5 16 311 38 + = += += 14. 32 10 5 1 8 10 5 18 2 16 17 + = += += += 15.( ) ( )3 36 3 1 8 6 2 86 8 82 86 + = += += += Appendix ASSM: Intermediate Algebra 382 16.( ) ( )310 4 2 5 10 4 8 510 32 522 517 + = += += += 17.5.4 7.1 2.4 1.8 5.4 17.04 1.822.44 1.820.64+ = + = = 18.( )( )2.9 4.1 9.9 24.7 6.42.9 5.8 24.7 6.416.82 24.7 6.416.82 3.85937512.960625 = = = = Section A.9 1.4 124 124 43xxx=== 2.2 102 2 10 212xxx = + = += 3.5 3 135 3 3 13 35 105 105 52xxxxx + = + = == = 4.9 4 59 4 4 5 49 99 99 91xxxxx = + = + == = 5.( ) 2 1 72 2 72 2 2 7 22 52 52 252xxxxxx+ =+ =+ = === 6.( ) 3 4 83 12 83 12 12 8 123 203 202 202 202 210x xx xx xx xx x x xxxx = + = + + = + += + = + === 7.( ) 3 5 93 5 453 5 5 45 56 3 456 3 3 45 36 486 486 68x xx xx x x xxxxxx = = + + = + + = + = +=== 8.( ) 6 2 3 4 36 12 3 4 39 12 4 4x x x xx x x xx x + = + + = + = 9 12 4 4 4 45 12 45 12 12 4 125 85 85 585x x x xxxxxx = = + = +=== SSM: Intermediate AlgebraAppendix A 383 9.2.17 6.88 3.22 9.192.17 6.88 3.22 3.22 9.19 3.221.05 6.88 9.191.05 6.88 6.88 9.19 6.881.05 16.071.05 16.071.05 1.0515.3048x xx x x xxxxxx = + = + = + = + == 10.( ) 3.4 1.2 8.8 4.73.4 4.08 8.8 4.73.4 4.08 8.8 8.8 4.7 8.85.4 4.08 4.75.4 4.08 4.08 4.7 4.085.4 8.785.4 8.785.4 5.41.62593x xx xx x x xxxxxx = + = + = + = + = + == = 11. 2 1 53 4 122 1 512 123 4 12xx+ = + = 2 1 512 12 123 4 128 3 58 3 3 5 38 28 28 814xxxxxx + = + =+ = === 12. 3 3 15 10 2x =( )3 3 110 105 10 23 3 110 10 105 10 22 3 3 52 6 3 52 9 52 9 9 5 92 142 142 27xxxxxxxxx = = = = = + = +=== Section A.10 1.2 82 8x yy x+ == + 2.3 183 183 18x yy xy x = = += 3.5 2 105 2 105 2 105 5 5225w tw tw tw t+ == += += + 4.( ) 3 2 13 6 13 6 13 73 73 3 31 73 3w tw tw tw tw tw t = = = += += += + Appendix ASSM: Intermediate Algebra 384 5.2.5 8.18.1 2.58.1 2.52.5 2.5 2.50.4 3.240.4 3.24p dp dp dp dd p= + =+ =+ == + 6.1.6 10.21.6 10.21.6 10.21.6 10.21.6 1.6 1.60.625 6.375p dd pd pd pd p= ++ == += += + 7.4 3 2 93 6 93 6 93 3 32 3x y xy xy xy x + = += += += + 8.4 3 2 96 3 96 3 96 3 96 6 61 32 2x y xx yx yx yx y + = + + = = + = + = 9.( ) 3 4 2 53 4 2 104 104 104 4 41 54 2a b aa b ab ab ab a+ = ++ = += += += + 10.7 3 08 3 08 38 38 838a b aa ba ba ba b + = ==== 11. 1 3 52 4 81 3 58 82 4 81 3 58 8 82 4 84 6 56 4 52 53 6x yx yx yx yy xy x = = = = = += 12. 3 2 14 3 43 2 112 124 3 43 2 112 12 124 3 49 8 38 9 39 38 8x yx yx yx yy xy x = = = = = += Section A.11 1.( ) 5 4 x and5 20 x ( ) ( ) 5 4 5 5 45 20x xx = = Equivalent expressions. 2.8 0 x + =and8 x = 8 08 8 0 88xxx+ =+ = = Equivalent equations. The solution sets are the same. 3.4 3 8 x x +and 212 8 x +( ) 4 3 8 4 3 88x x xx + = += + Neither, 28 12 8 x x + + . 4.( ) 3 1 7 x + +and3 8 x +( ) 3 1 73 3 73 10xxx+ ++ ++ Neither,3 10 3 8 x x + +SSM: Intermediate AlgebraAppendix A 385 5.( ) 4 2 x +and4 8 0 x + =Neither. One is an expression and the other is an equation. 6.( ) 3 2 5 x and6 15 x +( ) ( ) ( ) 3 2 5 3 2 3 56 15x xx = = + Equivalent expressions. 7.3 1 16 x + =and3 15 x =3 1 163 1 1 16 13 15xxx+ =+ = = Equivalent equations. 8.( ) 2 3 5 25 x + =and2 23 x =( )( )2 3 5 252 3 203 1013xxxx + = = == 2 23232xx== Neither. The solution sets are different. 9.( ) 3 4 18 x = and2 x =( ) 3 4 183 12 183 3010xxxx = + = = = Neither. The equations have different solution sets. 10. 23 5 2 x x + and 22 2 5 x x x + +2 22 2 5 2 6 2 x x x x x + + = + Neither, 2 23 5 2 2 6 2 x x x x + + .