Arbeitsblatt zu Einfache Gleichungen 1 (mit Lösungen), Übungen von Mathematik

Nur auf Docsity: Lade Arbeitsblatt zu Einfache Gleichungen 1 (mit Lösungen) und mehr Übungen als PDF für Mathematik herunter! Einfache Gleichungen 1 a) x + 3 = 8 b) x + 2 = 12 c) x + 9 = 18 d) x + 4 = 5 e) x + 22 = 44 f) x + 28 = 30 1. g) x + 7 = 2 h) x + 8 = –4 i) x + 2 = –12 a) x – 1 = 2 b) x – 3 = 5 c) x – 4 = 11 d) x – 8 = 9 e) x – 2 = 13 f) x – 12 = 22 2. g) x – 7 = –11 h) x – 9 = –14 i) x – 1 = –19 a) x 5 15⋅ = b) x 2 8⋅ = c) x 7 21⋅ = d) 3 x 27⋅ = e) 9 x 45⋅ = f) 8 x 64⋅ = 3. g) x 2 4,2⋅ = h) 5 x 12,5⋅ = i) 9 x 1,8⋅ = xa) 2 2 = xb) 1 5 = xc) 9 8 = xd) 9 5 = xe) 7 7 = xf ) 9 6 = 4. xg) 0,3 10 = xh) 1,1 4 = xi) 0,8 8 = a) x – 2 = 5 b) 3 + x = 1 c) x 4 12 = − d) 3 x 3,6⋅ = e) x ( 4) 3,6⋅ − = − xf ) 1,1 3 = − 5. g) x + 1,8 = 2,2 h) x – 3,6 = 1,5 i) 3 x 1,5− ⋅ = − a) 3 – x = 4 b) 2 – x = 8 c) 7 – x = 5 d) 9 – x = –3 e) 5 – x = – 8 f) –3 – x = –1 6. g) –2 – x = 6 h) 3 – x = 5 i) –4 – x = 12 a) 3x + 4 = 16 b) 2x + 3 = 13 c) 4 + 5x = 19 d) 4x – 1 = 15 e) 9x – 8 = 19 f) 10x – 15 = 45 7. g) 5 – 2x = 15 h) 3 – 6x = 21 i) 9 – 5x = –36 xa) 4 3 2 − = xb) 3 2 3 + = xc) 3 4 5 − = xd) 8 2 5 + = xe) 4 5 8 + = 3xf ) 2 5 4 + = 8. 2xg) 1 5 5 − = 5xh) 4 1 6 − + = 2xi) 9 11 9 + = 12a) 3 x = 6b) 3 x = 15c) 15 x =9. 14d) 7 x = 16e) 4 x = 49f ) 7 x = Seite 2 Gleichungen mit Additions- und Subtraktionsklammern a) 2x + (3x + 4) = 19 b) 12x + (3x + 4) + (2x + 3) = 41 c) 12x – 4 + (3x + 1) = 27 d) 8x – 3 + (x + 1) = 2x + 7 + (4x + 3) 1. e) 4 – (3x – 2) + 5x = 4 – (x + 1) f) (4x – 4) – 8 = –(3x – 2) a) 12x + (13x – 19) – (11x – 15) = 25 – (17 – 13x) b) (3x + 7) – 6 = 12x – (x + 4) – (4x – 5) c) (5x – 3 ) – (2x – 4) = – (x + 3) – (x + 5) + (x + 3) d) 12 – (5x + 8) – (8x – 12) = 14x – 25 – (3x – 8) + (7x + 2) e) –(3x – 5) – (7x – 24) = 3 + (x + 1) – (2x – 7) 2. f) 12x – (3x + 8) + (39 – 5x) = 14 + (25x – 8) – (41 – x) a) 12x – 3 – (23x – 48) + (x + 93) = 58x – (24x – 44) + 6 b) –(19x + 51) – (11x + 4) = –(39x + 45) + (8x – 7) – 24 c) 24 – (14x – 8) – (3 + 12x) = 4 – (8x + 11) d) 3,7 – (8,1x + 5,4) – (2,6x + 8,3) = –3,1x + (8 – 1,6x) e) (4,5x + 56) – (2,25x – 7) – (300 – 3x) = – (0,75x – 3) 3. f) 3,5x – 6 – (4 – 2x) = (2,4x – 9,4) – (1,2x – 25,2) Gleichungen – Klammer mal Zahl a) 7(x – 2) = 49 b) 7(5x + 2) + 9 = 58 c) 15(8x – 24) = 120 d) 6(3x – 25) = 12 1. e) 12(5x – 2) = 48 + 12x f) 3(4x + 18) = 6x + 108 a) 23(2x + 5) = 6x + 315 b) 17(5x + 3) = 401 + 35x c) 16(2x – 3) = 5(4x + 16) + 4 d) 12(8x – 25) = 5(16x + 40) – 20 2. e) 13(20 – 5x) = 15(30 – 5x) f) 14(7x – 14) + 3 = 12(8x + 20) + 1 a) 5(3x – 4) = 7(2x – 3) b) 3(6x – 9) = 9(2x – 3) c) 8(3x – 5) = 60 + 20x d) 5x – 4(2 – 3x) = 22 + 7x 3. e) 3(x + 6) + 2(x + 1) = 40 f) 8(3x – 5) = 60 + 20x a) 5x – 4(2 – 3x) = 22 + 7x b) 6(1 – 3x) + 7(4x – 3) = 35 c) 18q + 3 = 3(6,1q – 5) d) 5(x + 1,2) – 4 = 10x + 3 4. e) 4(x + 9) – 34 = 2(x – 4) + 11 f) 8 – 10x – 2 = 8 – 5(x + 1,4) Gleichungen – Klammer mal Klammer a) (20 + x)(20 – x) = (x + 2)(46 – x) b) (x + 5)(5 – x) = (12 + x)(4 – x) + 1 c) (x – 5)(x + 8) = (x – 2)(x + 1) + 6 d) (x + 12)(x + 5) = (x – 8)(x + 7) – 10 1. e) (x – 8)(x – 15) = (x – 8)(x – 25) f) (x + 9)(x – 17) = (x – 5)(x – 10) a) (x +2)(x – 3) = x(x – 2) b) (2x + 4)(2x – 5) = (4x – 3)(x + 2) c) (2x – 4)(3 – x) = (x + 4)(2 – 2x) d) x(3x + 2) = (3x – 6)(x + 2) 2. e) (x – 2)(x + 5) = (x + 6)(x – 1) f) (x – 2)(2x + 3) = (4 – x)(5 – 2x) + 1 a) (12 – x)(15 + x) = (8 – x)(9 + x) b) (15 – x)(20 + x) = (30 – x)(5 + x) c) (x + 20)(x – 30) = (x – 10)(x + 40) d) (9 + x)(15 + x) = (3 + x)(5 + x) e) (2x – 15)(3x + 4) = (6x – 4)(x + 12) – 117 3. f) (x + 2)(3 – x) = (5 + x)(7 – x) + 2(x + 29) Seite 5 19. ax + b + 2ax – 12b = 5ax – 3b – 6ax 20. (3a – x)² = (5a – x)² 21. (5 + x)²(a – b) = (5 + x)²(a + b) – 2bx² Gleichungen mit 1 Variablen – verm. Übungen 3 Bestimme die Lösungsmenge zu folgenden Gleichungen. a) 12x – 56 = 16 b) 5x + 39 = –26 4c) x 40 48 5 + = 3d) 1 x 4,2 7,4 5 + = e) 7x – 4 + 2x = 52 – 5x f) 40 – 2x + 5x = 68 + x 1. g) 22x + 4(9 – 3x) = 46 h) 4(3x – 5) + 30 = 46 a) 18x – 75 + 3x + 128 – 7x = 68 – 8x – 25 + 14x b) 113x + 73 – 5x – 16 = 23x + 85 – 33x + 45 + 62x + 151 c) 6x – 2(x – 16) = 5 – 3(11 – x) + 60 d) 4x – 5(x – 12) = 40 + 9(9 – x) – 11 3 2e) (16x 24) 6(3x 4) (27x 18) 6x 3 4 3 + + − = + + − 2. f) 3x – 15 + 2x = 18 + 4x + 25 a) 17x – 33 + 12x – 16 = 4x + 56 + 10x b) –22x + 36 + 18x – 6 = 16x + 55 + 12x – 89 c) 4x – 22 + 3x – 45 = 8 – 2x + 26 + 5x – 1 d) 6x + 36 – 2x + 45 = 3x + 88 – 8x + 47 e) 12x – 66 – 34 + 2x = 8x – 35 + 2x + 99 3. f) –12x + 25 + 6x – 38 = 66 + 2x – 22 + 3x – 12x a) 66x + 14 – 39 + 12x – 100 = –12x – 47 + 23x + 56 b) 22x + 48 – 55x – 55x = 36 – 45 + 12x – 43 c) –22 + 14x – 33 + 10x – 77 + 25x = 88 – 14x + 65 – 5 + 35 d) –78 + 66x – 21x + 20 – 47 + 88x = 10x – 36 – 36x + 90 e) 55x – 44x – 12x –12x + 96 = 12x + 99 – 178 – 66x – 30 4. f) –44 – 25x + 29 – 32x – 98x + 14x = –47x + 66 – 58x + 124 + 11 a) 12x – 33 + 20x – 78x + 36 – 48 + 30x – 45x + 558 – 14x – 605 – 58 = 0 b) –33x – 44x + 54 – 88 + 12x – 100 + 222x = 12 – 45x + 999 – 10x + 305 + 34 c) 36x – 78 + 61x – 69 – 78 + 22x – 47x = 369 – 44x + 45 – 12x + 78 + 120x + 11 d) –987x – 564 + 55x – 123 + 78 = –987x + 258 – 25x + 478 + 255 e) 16x² – 56x + 22 – 851 – 951 + 357x = 16x² + 698 – 14x + 548 – 20x – 11 5. f) –65a + 58 – 36a + 587 – 33a = 698 + 14a – 587a + 698 – 32a +191 a) –789v + 258 – 11v + 456 – 894 = 336v + 201 – 45v + 710 b) 66z + 587 – 65z + 32z – 784 = –35z + 368 – 45z + 125 – 12 c) – 47y + 569 – 45y – 55y + 231 = –147y + 987 – 36y + 444 + 89 d) 665m – 478 – 365m + 884 – 320m = 6987 – 358 – 12m – 3365 + 6 e) –254a + 369 – 258 + 458a – 369 = –540a + 3320 + 142 6. f) –258x + 5873 – 3369 + 368x – 897 – 321x + 33 = 1007 Seite 6 Einfache Gleichungen 1 – Lösungen a) x + 3 = 8 b) x + 2 = 12 c) x + 9 = 18 L = { 5 } L = { 10 } L = { 9 } d) x + 4 = 5 e) x + 22 = 44 f) x + 28 = 30 L = { 1 } L = { 22 } L = { 2 } g) x + 7 = 2 h) x + 8 = –4 i) x + 2 = –12 1. L = { –5 } L = { –12 } L = { –14 } a) x – 1 = 2 b) x – 3 = 5 c) x – 4 = 11 L = { 3 } L = { 8 } L = { 15 } d) x – 8 = 9 e) x – 2 = 13 f) x – 12 = 22 L = { 17 } L = { 15 } L = { 34 } g) x – 7 = –11 h) x – 9 = –14 i) x – 1 = –19 2. L = { –4 } L = { –5 } L = { –18 } a) x 5 15⋅ = b) x 2 8⋅ = c) x 7 21⋅ = L = { 3 } L = { 4 } L = { 3 } d) 3 x 27⋅ = e) 9 x 45⋅ = f) 8 x 64⋅ = L = { 9 } L = { 5 } L = { 8 } g) x 2 4,2⋅ = h) 5 x 12,5⋅ = i) 9 x 1,8⋅ = 3. L = { 2,1 } L = { 2,5 } L = { 0,2 } xa) 2 2 = xb) 1 5 = xc) 9 8 = L = { 4 } L = { 5 } L = { 72 } xd) 9 5 = xe) 7 7 = xf ) 9 6 = L = { 45 } L = { 49 } L = { 54 } xg) 0,3 10 = xh) 1,1 4 = xi) 0,8 8 = 4. L = { 3 } L = { 4,4 } L = { 6,4 } a) x – 2 = 5 b) 3 + x = 1 xc) 4 12 = − L = { 7 } L = { –2 } L = { –48 } d) 3 x 3,6⋅ = e) x ( 4) 3,6⋅ − = − xf ) 1,1 3 = − L = { 1,2 } L = { 0,9 } L = { –3,3 } g) x + 1,8 = 2,2 h) x – 3,6 = 1,5 i) 3 x 1,5− ⋅ = − 5. L = { 0,4 } L = { 5,1 } L = { 0,5 } a) 3 – x = 4 b) 2 – x = 8 c) 7 – x = 5 L = { –1 } L = { –6 } L = { 2 } d) 9 – x = –3 e) 5 – x = – 8 f) –3 – x = –1 L = { 12 } L = { 13 } L = { –2 } g) –2 – x = 6 h) 3 – x = 5 i) –4 – x = 12 6. L = { –8 } L = { –2 } L = { –16 } Seite 7 a) 3x + 4 = 16 b) 2x + 3 = 13 c) 4 + 5x = 19 L = { 4 } L = { 5 } L = { 3 } d) 4x – 1 = 15 e) 9x – 8 = 19 f) 10x – 15 = 45 L = { 4 } L = { 3 } L = { 6 } g) 5 – 2x = 15 h) 3 – 6x = 21 i) 9 – 5x = –36 7. L = { –5 } L = { –3 } L = { 9 } xa) 4 3 2 − = xb) 3 2 3 + = xc) 3 4 5 − = L = { 14 } L = { –3 } L = { 35 } xd) 8 2 5 + = xe) 4 5 8 + = 3xf ) 2 5 4 + = L = { –30 } L = { 8 } L = { 4 } 2xg) 1 5 5 − = 5xh) 4 1 6 − + = 2xi) 9 11 9 + = 8. L = { 15 } L = { 6 } L = { 9 } 12a) 3 x = 6b) 3 x = 15c) 15 x = L = { 4 } L = { 2 } L = { 1 } 14d) 7 x = 16e) 4 x = 49f ) 7 x = 9. L = { 2 } L = { 4 } L = { 7 } Gleichungen mit Additions- und Subtraktionsklammern Lösungen a) 2x + (3x + 4) = 19 b) 12x + (3x + 4) + (2x + 3) = 41 L = { 3 } L = { 2 } c) 12x – 4 + (3x + 1) = 27 d) 8x – 3 + (x + 1) = 2x + 7 + (4x + 3) L = { 2 } L = { 4 } e) 4 – (3x – 2) + 5x = 4 – (x + 1) f) (4x – 4) – 8 = – (3x – 2) 1. L = { –1 } L = { 2 } a) 12x + (13x – 19) – (11x – 15) = 25 – (17 – 13x) L = { 12 } b) (3x + 7) – 6 = 12x – (x + 4) – (4x – 5) L = { 0 } c) (5x – 3 ) – (2x – 4) = – (x + 3) – (x + 5) + (x + 3) L = { –1,5 } d) 12 – (5x + 8) – (8x – 12) = 14x – 25 – (3x – 8) + (7x + 2) L = { 1 } e) – (3x – 5) – (7x – 24) = 3 + (x + 1) – (2x – 7) L = { 2 } f) 12x – (3x + 8) + (39 – 5x) = 14 + (25x – 8) – (41 – x) 2. L = { 3 } a) 12x – 3 – (23x – 48) + (x + 93) = 58x – (24x – 44) + 6 L = { 2 } b) – (19x + 51) – (11x + 4) = –(39x + 45) + (8x – 7) – 24 3. L = { –21 } Seite 10 a) 8 – 7(3x + 2) = 9x – 6(5x + 1) L = D b) 3x – 2(5x – 8) = 9 – 4(3x + 7) 8. L = { –7 } a) 5(3x – 8) + 3(7x + 6) = 6(8x + 3) – 4(2x + 5) L = { –5 } b) 8(4x + 3) – 5(6x – 5) = 4(9x + 4) – 7(4x – 5) 9. 1L 3 ⎧ ⎫= −⎨ ⎬ ⎩ ⎭ a) 5(8x + 5) – 4(3x + 4) – 2(11x – 17) = 25 – 3(5x – 7) + 6(3x – 2) L = { –3 } b) (2x – 3)7 – (x – 2)6 – (5x + 6)2 = 26 – (3x – 4)4 + (6x – 5)3 10. L = { –6 } a) (x + 4)(3x – 7) = (x – 2)(3x + 8) b) (x + 5)(x + 2) = (x + 6)(x – 1)11. L = { 4 } L = { –8 } a) (x – 4)(6 – x) = (x – 3)(8 – x) b) (x + 3)(2x + 5) = (x + 7)(2x – 1)12. L = { 0 } L = { 11 } a) (x – 2)(x + 3) = (x + 4)(x – 5) b) (x + 1)(4x – 25) = (2x – 5)(2x – 8)13. L = { –7 } L = { 13 } a) (x + 5)(x – 3) = (x + 6)(x – 2) b) (x – 7)(x – 4) = (x – 5)(x – 2)14. 3L 2 ⎧ ⎫= −⎨ ⎬ ⎩ ⎭ 9L 2 ⎧ ⎫= ⎨ ⎬ ⎩ ⎭ a) (x – 4)(x – 3) = x² – 7x + 12 b) (2x – 5)(x + 1) = 2x² – 3x – 515. L = D L = D a) (5x – 6)(2x + 3) + (2x + 3)(3x – 2) = 2x(8x + 1) L = { 4 } b) (9x – 2)(2x – 5) + (3x + 4)(5x + 3) = 3x(11x – 3) 16. L = { 2 } a) (3x – 4)(2x – 1) – (3x + 1)(x – 3) = (3x – 1)(x – 1) L = { –6 } b) (2x + 1)(3x – 1) – (2x + 11)(2x – 5) = (x – 6)(2x – 3) 17. L = { –9 } a) (5x – 3)(2x – 3) – 2(4x – 1)(x – 3) = (2x – 3)(x + 5) L = { 9 } b) (3x + 1)(4x – 5) – 3(x – 3)(2x – 1) = (6x + 1)(x + 1) 18. L = { 5 } a) (x + 3)² + (x – 4)² = (x – 1)² + (x + 2)² L = { 5 } b) (3x + 5)² + (2x – 3)² = (4x + 1)² – 3(x² – 1) 19. L = { –3 } Seite 11 a) (x + 1)² – (x – 3)² = (x – 2)² – (x – 4)² L = { –1 } b) (4x + 3)² – (5x – 2)² = 6(x + 9) – (3x – 7)² 20. L = { 0 } a) (x + 1)(x – 1) – (x – 3)² = (x + 4)² – (x – 2)(x + 2) L = { –15 } b) (x – 3)² – (x + 6)(x – 6) = (2x + 3)(2x – 3) – 4(x² – 15) 21. L = { –1 } a) (2x + 1)² – (x – 4)² = (3x – 2)² – (2x + 1)(2x – 1) – 2(x² – 7x + 10) L = { 0 } b) (2x – 3)² + (3x + 5)² = (4x + 3)² – (3x – 2)(x + 6) – (2x – 7) 22. L = { –0,5 } Gleichungen mit 1 Variablen – verm. Übungen 2 – Lösungen 1. 5x + 4 – 6x + 8 = 3x + 4 – 8x – 7 + 3x L = { –15 } 2. 18 – x – 15 + x + 2x = 18 – x + 19 + 3x – 1 – x L = { 33 } 3. x – (x + 3) + x – 5 = 6 – (x – 4) + (x + 1) L = { 19 } 4. 25x + 14 – (3x – 8) = 9x – (6x + 3) – 4x + (2 + 22x) L = { –23 } 5. 5 – [x + 6 – (3 – x)] – 10x = 6x – [(3x + 2) – x] – 17x L = { –4 } 6. 4(x – 3) + 5(x + 6) = 3 – 5(x + 3) + 13x L = { –30 } 7. 5x – (6 – 3x) + 6(3x – 8) = 23x – 4(x – 5) + 6x L = { 74 } 8. 172x + 19(24x – 17) = 207x – 18(61 – 18x) + 96x L = { –775 } 9. 12(x + 13) – 14x + 5(x + 12) – 4(x + 3) = 0 L = { 204 } 10. 9x – {5x – [4x – (3x – 2) – 3] – 4} = 5x – 6 + x L = { 9 } 11. x + 15 + 5(2x – 10) = 4x – (5 + x) + 2 Seite 12 L = { 4 } 12. 17(3x – 8) – [4x – (3 – x)] = 46x – 1 – 3(x + 2) L = { 42 } 13. 31x – 58 + 4x – 16 = 5x + 24 + 9x – 18 + 4 L = { 4 } 14. 52(17x – 28) + 92(44 – 53x) = –51x + 20563 + 29(71x + 1) L = { –3 } 15. 3x + 6(5x + 8) – 6 – (3 + x) – 6(x – 1) – 23x = 0 L = { –15 } 16. 2x + 3a – 5b + 4a – x = 4(a + b) L = { –3a + 9b } 17. 12x – a – (a – x) = 14x + (a + b) – 3x + b L = { b + 1,5a } 18. a + a² – b² – x = x – a + a² – b² L = { a } 19. ax + b + 2ax – 12b = 5ax – 3b – 6ax 2bL (mit a 0) a ⎧ ⎫= ≠⎨ ⎬ ⎩ ⎭ 20. (3a – x)² = (5a – x)² L = { 4a } (mit a 0)≠ 21. (5 + x)²(a – b) = (5 + x)²(a + b) – 2bx² L = { –2,5 } Gleichungen mit 1 Variablen – verm. Übungen 3 – Lösungen Bestimme die Lösungsmenge zu folgenden Gleichungen. a) 12x – 56 = 16 b) 5x + 39 = –26 L = { 6 } L = { –13 } 4c) x 40 48 5 + = 3d) 1 x 4,2 7,4 5 + = L = { 10 } L = { 2 } e) 7x – 4 + 2x = 52 – 5x f) 40 – 2x + 5x = 68 + x L = { 4 } L = { 14 } g) 22x + 4(9 – 3x) = 46 h) 4(3x – 5) + 30 = 46 1. L = { 1 } L = { 3 }