UE lineare Gleichungen 01 3. Klasse
1. Löse folgende Gleichungen (G=Q):
(a) 4x−5 = (x+ 3)·4 (b) x·(x−2)−3x=x2+ 5 (c) 2·[3−4·(x+ 2)−2] + 12 ·[2−4·(x−1)] = 0
2. Löse:
(a) 7(8x+ 3)−(5x−3)·8 = 0 (b) 2(x+a) = 6−3x+ 2a (c) 12 ·(4x+13)− 14(12x+ 1) = (9x−14)· 13
3. Bestimme die Lösungsmenge folgender Gleichung (G=Q):
(a) (5x+ 4)(5x−4)−(2−2x)2 = (4x−1)2+ (2x−8)(4x+ 2)−x(3x−4) (b) 2 (x+ 3)2− 13x−122
= 100 (1,2x−0,6)(1,2x+ 0,6)−19x2−2x 71x− 16 (c) (11x−2)2−(7−9x)2 = (6x+ 13)2 + (2x−5)(2x+ 5)
(d) 5(3−5x)−[4(2 + 3x)−10] + 9x= 3x−1
(e) (2x−5)(2x+ 5) + (7−9x)2 = (11x+ 2)2−(6x+ 13)2 (f) (1−5x)2+ 3x(8x+ 3) = (7x−1)2+ 3(1−x)
(g) (2x−5)(2x+ 5) + (7−9x)2 = (11x+ 2)2−(6x+ 13)2 (h) (1−5x)2+ 3x(8x+ 3) = (7x−1)2+ 3(1−x)
(i) (2−x)2 + 2·(4x−2)−5·(2−x) = (x+ 3)2 (j) 3·(4x−2) + 112 −x2
= x+132
+ 3·(2−3x)
4. Gib zu folgenden Gleichungen jeweils die Lösungsmenge L1zur Grundmenge G1 =Nund L2zu G2 =Qan.
(a) (8x−1)(x+ 3) = 8(x−2)2 (b) 16(x−2) + 23x= 13(52x−1)
(c) 6(3x−1)−7(2x−1) = 4(x+ 9)−42
5. Löse:
(a) 3,5x+ 7,7 = 7(2,9−x) (b) (z−5)(z−6)−z(z−8) = 0 (c) b−11 = 3
(d) 3t − t+812 = 1160
(e) (2x+ 6)2 = 5x2−(x−2)2 (f) 1+xax = 2
(g) 2x1 − 3x1 =−56 (h) (7−23)y = 7(y− 23)
(i) z−1z =−1−zz (j) (b− 27) = 0,5 (k) 0 = 2(ab+ac+bc)
(l) 1b + 1g = f1 (m) A= a+b2 ·h
(n) w+5w−2 = 0
(o) (s− 23)·(2s−114) = 0
(p) (12+2x)·(12−2x)+2x= (2−x)·x−1312
linGlg01 1 http://mone.denninger.at
UE lineare Gleichungen 01 3. Klasse
LÖSUNGEN:
1. (a) L={} (b) L={−1} (c) L={−1,1}
2. (a) x=−21316 (b) x= 115 (c) x= 0 3. (a) 18
(b) −42348 (c) L={−24174} (d) L={1831}
(e) L={1312} (f) L={163} (g) L={1312} (h) L={163}
(i) x= 613 (j) x= 355624
4. (a) L1 ={}, L2 ={117 } (b) L1 =G1, L2 =G2 (c) L1 =L2 ={}
5. (a) x= 1,2 (b) z = 10 (c) b = 113 (d) t= 325 (e) x=−2
(f) x= a−22 ,a= 2x + 2 (g) x=−15
(h) y= 7
(i) {}
(j) b1 = 1114,b2 =−143
(k) a=−b+cbc ,b =−a+cac ,c=−a+bab (l) f = b+gbg ,b= g−ff g ,g = b−fbf (m) h= a+b2A,a= 2Ah −b,b = 2Ah −a
(n) w=−5 (o) s1 = 23,s2 = 58 (p) x1 = 23,x2 =−23
linGlg01 2 http://mone.denninger.at
