# X 75 33 02 x 42 x 42 02 x 21 1 1 2 5 x 3 4 x 2 x 2 4

• Notes
• 52

This preview shows page 40 - 45 out of 52 pages.

x+ 7.5 = 3.3-0.2x= -4.2x=±4.2±0.2x= 21 (1-1)2.5x3-4+x2=x±24+ 1125x3- 12(4+x)2= 12(x±2)4+ 1220x- 6(4 +x) = 3(x- 2) + 1220x- 24 - 6x= 3x- 6 + 1214x- 24 = 3x+ 611x= 30x=3011(1-1)3.3(2 -x) - 2±2x- 16 - 3x- 2±2x- 1-3x+ 4±2x- 1-5x±-5x²1[1,³)[1x(1-2)4.|y+ 9| < 5-5 <y+ 9 < 5-14 <y< -4(-14, -4)()y-14-4(1-3)
CHAPTER 1 REVIEW715.|3 - 2x|±5-5±3 - 2x±5-8±-2x±24²x²-1-1±x±4[-1, 4][]x-14(1-3)6.(A) 9 – 4i= 9 + (–4)iReal part: 9Imaginary part: –4iConjugate: 9 – (–4)i= 9 + 4i(B) 5i= 0 + 5iReal part = 0Imaginary part: 5iConjugate: 0 + (–5)i= –5i(C) –10 = –10 + 0iReal part: –10Imaginary part: 0Conjugate: –10 – 0i= –10(1-4)7.(A) (-3 + 2i) + (6 - 8i) = -3 + 2i+ 6 - 8i= 3 - 6i(B) (3 - 3i)(2 + 3i) = 6 + 3i- 9i2= 6 + 3i+ 9 = 15 + 3i(C)13±i5±3i=(13±i)(5±3i)(5+3i)(5+3i)=65+34i±3i225±9i2=65+34i+325+9=68+34i34= 2 +i(1-4)8.2x2- 7 = 02x2= 7x2=72x= ±72x= ±142(1-5)9.2x2= 4x2x2- 4x= 02x(x- 2) = 02x= 0x- 2 = 0x= 0x= 2(1-5)10.2x2= 7x- 32x2- 7x+ 3 = 0(2x– 1)(x– 3) = 02x- 1 = 0x- 3 = 0x=12x= 3(1-5)11.m2+m+ 1 = 0m=±b±b2±4ac2aa= 1b= 1c= 1m=±1±(1)2±4(1)(1)2(1)m=±1±±32m=±1±i32m= -12±32i(1-5)12.y2=32(y+ 1)2y2= 3(y+ 1)2y2= 3y+ 32y2- 3y- 3 = 0y=±b±b2±4ac2aa= 2b= -3c= -3y=±(±3)±(±3)2±4(2)(±3)2(2)y=3±334(1-5)
72CHAPTER 1 EQUATIONS AND INEQUALITIES13.5x±6-x= 05x±6=x5x- 6 =x20 =x2- 5x+ 6x2- 5x+ 6 = 0(x- 3)(x- 2) = 0x= 2, 3Check:5(2)±6- 2=?00=±05(3)±6- 3=?00=±0Solution: 2, 3(1-6)14.3±5xrepresents a real number exactly when 3 - 5xis positive or zero.We can write this as an inequality statement and solve forx.3 - 5x±0-5x±-3x²35(1-2)15.72±x=10±4xx2+3x±1072±x=10±4x(x±2)(x+5)Excluded values:x³2, -5-1(x– 2)(x+ 5)72±x= (x- 2)(x+ 5)10±4x(x±2)(x+5)1-7(x+ 5) = 10 - 4x-7x- 35 = 10 - 4x-3x= 45x= -15(1-1)16.u±32u±2=16-1±u3u±3u±32(u±1)=16-1±u3(u±1)Excluded value:u³16(u- 1)(u±3)2(u±1)= 6(u- 1)16- 6(u- 1)(1±u)3(u±1)3(u- 3) =u- 1 - 2(1 -u)3u- 9 =u-1 - 2 + 2u3u- 9 = 3u- 3-9 = -3No solution(1-1)
CHAPTER 1 REVIEW7317.x+38±5 -2±x324(x+3)8±120 - 24(2±x)33(x+ 3)±120 - 8(2 -x)3x+ 9±120 - 16 + 8x3x+ 9±8x+ 104-5x±95x²-19[-19,³)[-19x(1-2)18.|3x- 8| > 23x- 8 < -2or3x- 8 > 23x< 63x> 10x< 2orx>103(-³, 2)±103,±²³´µ·)(x2103(1-3)19.(1±2m)2±3|1 - 2m|±3-3±1 - 2m±3-4±-2m±22²m²-1-1±m±2[-1, 2]][-12m(1-3)20.(A)d(A,B) = |-2 - (-8)| = |6| = 6(B)d(B,A) = |-8 - (-2)| = |-6| = 6 (1-3)21.(A) (3 +i)2- 2(3 +i) + 3 = 9 + 6i+i2- 6 - 2i+ 3= 9 + 6i- 1 - 6 - 2i+ 3= 5 + 4i(B)i27=i26i= (i2)13i= (-1)13i= (-1)i= -i(1-4)22.(A) (2 -±4) - (3 -±9) = (2 -i4) - (3 -i9) = (2 - 2i) - (3 - 3i)= 2 - 2i- 3 + 3i= -1 +i(B)2±±13+±4=2±i13+i4=2±i3+2i=(2±i)(3+2i)(3±2i)(3±2i)=6±7i+2i29±4i2=6±7i±29+4=4±7i13=413-713i(C)4+±25±4=4+i25i4=4+5i2i=4+5i2iii=4i+5i22i2=4i±5±2=52- 2i(1-4)23.u+52±²³´µ2=54u+52= ±54u+52= ±52u= -52±52u=±5±52(1-5)24.1 +3u2=2uExcluded value:u´0u2+ 3 = 2uu2- 2u= -3u2- 2u+ 1 = -2(u- 1)2= -2u- 1 = ±±2u= 1 ±±2u= 1 ±i2(1-5)
74CHAPTER 1 EQUATIONS AND INEQUALITIES25.

Course Hero member to access this document

Course Hero member to access this document

End of preview. Want to read all 52 pages?