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8. ročníkLineární rovnice

Lineární rovnice

1) Vyřeš rovnice:

  1. 2x+3=72x + 3 = 7
  2. 3y−5=43y - 5 = 4
  3. 4a=124a = 12
  4. b+6=10b + 6 = 10
  5. 5c−1=95c - 1 = 9
  6. 8=2d+28 = 2d + 2

2) Najdi řešení rovnic:

  1. 3x+2=x+83x + 2 = x + 8
  2. 5y−1=2y+55y - 1 = 2y + 5
  3. 4a+3=9−2a4a + 3 = 9 - 2a
  4. 6b−4=8−b6b - 4 = 8 - b
  5. 7c+2=11−c7c + 2 = 11 - c
  6. 15−3d=d+315 - 3d = d + 3
  7. 2e+7=13−e2e + 7 = 13 - e

3) Vypočítej neznámou:

  1. 2(x+1)+3=x+72(x + 1) + 3 = x + 7
  2. 3(y−2)−1=2y−53(y - 2) - 1 = 2y - 5
  3. 4a−(a+3)=9−2a4a - (a + 3) = 9 - 2a
  4. 5b+2(b−1)=8+b5b + 2(b - 1) = 8 + b
  5. 6c−3=2(c+3)−16c - 3 = 2(c + 3) - 1
  6. 10−2(d+1)=3d−410 - 2(d + 1) = 3d - 4
  7. 3(e−2)+4=11−e3(e - 2) + 4 = 11 - e

4) Vyřeš rovnice:

  1. 3(x−2)+5=2x+13(x - 2) + 5 = 2x + 1
  2. 4(y+1)−3=5y−84(y + 1) - 3 = 5y - 8
  3. 5a−2(a−3)=12−a5a - 2(a - 3) = 12 - a
  4. 2(b+4)+3b=18−b2(b + 4) + 3b = 18 - b
  5. 7c−(2c+1)=3(c+2)7c - (2c + 1) = 3(c + 2)
  6. 14−3(d−1)=2d+514 - 3(d - 1) = 2d + 5
  7. 4(e−1)+6=15−2e4(e - 1) + 6 = 15 - 2e
  8. 9−2(f+2)=f−39 - 2(f + 2) = f - 3

5) Najdi hodnotu neznámé:

  1. 2(2x+1)−3=x+62(2x + 1) - 3 = x + 6
  2. 3(3y−2)+4=2y+93(3y - 2) + 4 = 2y + 9
  3. 4a−2(a+1)=3(a−2)4a - 2(a + 1) = 3(a - 2)
  4. 5(b−1)+2b=4(b+1)+15(b - 1) + 2b = 4(b + 1) + 1
  5. 6c−(3c+2)=2(c+3)−46c - (3c + 2) = 2(c + 3) - 4
  6. 16−2(2d−1)=3d+216 - 2(2d - 1) = 3d + 2
  7. 2(4e−3)+5=3(e+1)+22(4e - 3) + 5 = 3(e + 1) + 2
  8. 7−3(f+2)=2(f−1)−17 - 3(f + 2) = 2(f - 1) - 1

6) Vyřeš následující rovnice:

  1. 4(x−3)+7=2(x+1)4(x - 3) + 7 = 2(x + 1)
  2. 5(y+2)−1=3(y−2)+45(y + 2) - 1 = 3(y - 2) + 4
  3. 6a−3(a−4)=2(a+5)−16a - 3(a - 4) = 2(a + 5) - 1
  4. 3(2b+1)−4=2(b−3)+73(2b + 1) - 4 = 2(b - 3) + 7
  5. 8c−2(c+3)=4(c−1)+28c - 2(c + 3) = 4(c - 1) + 2
  6. 12−2(3d−2)=d+812 - 2(3d - 2) = d + 8
  7. 3(2e−1)+5=4(e+2)−13(2e - 1) + 5 = 4(e + 2) - 1

7) Vypočítej neznámou:

  1. 5(2x−1)+3=3(x+4)5(2x - 1) + 3 = 3(x + 4)
  2. 2(3y+2)−5=4(y−1)+32(3y + 2) - 5 = 4(y - 1) + 3
  3. 7a−4(a−2)=3(a+3)−17a - 4(a - 2) = 3(a + 3) - 1
  4. 4(2b−3)+6=2(b+5)+24(2b - 3) + 6 = 2(b + 5) + 2
  5. 9c−3(c+1)=5(c−2)+49c - 3(c + 1) = 5(c - 2) + 4
  6. 18−3(2d+1)=d+518 - 3(2d + 1) = d + 5
  7. 2(5e−2)+7=3(2e+1)+12(5e - 2) + 7 = 3(2e + 1) + 1
  8. 11−2(3f−1)=f−611 - 2(3f - 1) = f - 6

8) Najdi řešení daných rovnic:

  1. 3(4x+2)−7=2(3x−1)+53(4x + 2) - 7 = 2(3x - 1) + 5
  2. 4(2y−3)+1=3(y+2)−44(2y - 3) + 1 = 3(y + 2) - 4
  3. 8a−2(3a+1)=4(a−2)+38a - 2(3a + 1) = 4(a - 2) + 3
  4. 2(5b−4)+6=3(2b+1)−12(5b - 4) + 6 = 3(2b + 1) - 1
  5. 10c−3(2c−1)=2(c+4)+710c - 3(2c - 1) = 2(c + 4) + 7
  6. 15−2(4d+1)=3d−215 - 2(4d + 1) = 3d - 2
  7. 3(3e−2)+8=2(4e+1)−13(3e - 2) + 8 = 2(4e + 1) - 1
  8. 13−3(2f−3)=f+413 - 3(2f - 3) = f + 4
  9. 2(4g+1)−9=3(2g−1)+22(4g + 1) - 9 = 3(2g - 1) + 2

9) Vyřeš tyto lineární rovnice:

  1. 2(5x−3)+4=3(2x+1)−12(5x - 3) + 4 = 3(2x + 1) - 1
  2. 3(4y+1)−8=2(5y−3)+23(4y + 1) - 8 = 2(5y - 3) + 2
  3. 9a−4(2a−1)=5(a+2)−79a - 4(2a - 1) = 5(a + 2) - 7
  4. 4(3b−2)+5=2(4b+1)−34(3b - 2) + 5 = 2(4b + 1) - 3
  5. 12c−2(4c+3)=3(c−2)+112c - 2(4c + 3) = 3(c - 2) + 1
  6. 17−3(2d−2)=4d−117 - 3(2d - 2) = 4d - 1
  7. 2(6e−1)+3=5(2e−3)+82(6e - 1) + 3 = 5(2e - 3) + 8

10) Vypočítej hodnotu neznámé:

  1. 4(3x+1)−9=2(5x−2)+14(3x + 1) - 9 = 2(5x - 2) + 1
  2. 5(2y−4)+3=3(3y+1)−105(2y - 4) + 3 = 3(3y + 1) - 10
  3. 10a−3(3a−2)=2(a+5)−110a - 3(3a - 2) = 2(a + 5) - 1
  4. 2(6b−3)+7=4(2b+1)−52(6b - 3) + 7 = 4(2b + 1) - 5
  5. 14c−2(5c−1)=3(c−3)+814c - 2(5c - 1) = 3(c - 3) + 8
  6. 19−4(2d+1)=2d−319 - 4(2d + 1) = 2d - 3
  7. 3(4e−2)+5=5(2e+1)−23(4e - 2) + 5 = 5(2e + 1) - 2
  8. 16−2(5f−3)=f+716 - 2(5f - 3) = f + 7

11) Najdi řešení rovnic:

  1. 3(5x−2)+1=2(4x+3)−53(5x - 2) + 1 = 2(4x + 3) - 5
  2. 2(4y+3)−7=5(y−2)+62(4y + 3) - 7 = 5(y - 2) + 6
  3. 11a−2(4a−3)=3(a+4)−111a - 2(4a - 3) = 3(a + 4) - 1
  4. 5(3b−1)+2=4(2b+3)−75(3b - 1) + 2 = 4(2b + 3) - 7
  5. 16c−3(3c+2)=2(c−5)+316c - 3(3c + 2) = 2(c - 5) + 3
  6. 21−2(4d−3)=3d+421 - 2(4d - 3) = 3d + 4
  7. 4(3e−4)+9=2(5e+1)−34(3e - 4) + 9 = 2(5e + 1) - 3

12) Vyřeš následující lineární rovnice:

  1. 6(2x+1)−11=4(3x−2)+16(2x + 1) - 11 = 4(3x - 2) + 1
  2. 4(3y−5)+7=2(5y+1)−84(3y - 5) + 7 = 2(5y + 1) - 8
  3. 13a−3(3a+2)=2(a−4)+513a - 3(3a + 2) = 2(a - 4) + 5
  4. 7(2b−3)+4=3(4b+1)−67(2b - 3) + 4 = 3(4b + 1) - 6
  5. 18c−4(2c−1)=5(c+2)−318c - 4(2c - 1) = 5(c + 2) - 3
  6. 23−3(3d−1)=2d+723 - 3(3d - 1) = 2d + 7
  7. 5(2e−5)+12=3(3e+1)−45(2e - 5) + 12 = 3(3e + 1) - 4
  8. 19−2(4f+3)=f−819 - 2(4f + 3) = f - 8

13) Vypočítej neznámou:

  1. 7(2x−3)+5=3(4x+1)−97(2x - 3) + 5 = 3(4x + 1) - 9
  2. 3(5y+1)−10=4(3y−2)+13(5y + 1) - 10 = 4(3y - 2) + 1
  3. 15a−2(5a−4)=3(a+6)−515a - 2(5a - 4) = 3(a + 6) - 5
  4. 2(7b−1)+8=5(2b+3)−72(7b - 1) + 8 = 5(2b + 3) - 7
  5. 20c−3(4c+2)=2(c−7)+420c - 3(4c + 2) = 2(c - 7) + 4
  6. 25−2(5d−2)=3d+925 - 2(5d - 2) = 3d + 9
  7. 6(2e−4)+11=4(3e+1)−56(2e - 4) + 11 = 4(3e + 1) - 5

14) Najdi řešení těchto rovnic:

  1. 8(2x−1)−13=5(3x+1)−28(2x - 1) - 13 = 5(3x + 1) - 2
  2. 2(6y+1)−11=4(2y−3)+52(6y + 1) - 11 = 4(2y - 3) + 5
  3. 17a−4(3a−2)=2(a+7)−117a - 4(3a - 2) = 2(a + 7) - 1
  4. 5(4b−3)+7=3(5b+1)−95(4b - 3) + 7 = 3(5b + 1) - 9
  5. 22c−3(5c−1)=4(c−5)+222c - 3(5c - 1) = 4(c - 5) + 2
  6. 29−2(6d+1)=d+1029 - 2(6d + 1) = d + 10
  7. 3(5e−6)+15=2(7e+1)−43(5e - 6) + 15 = 2(7e + 1) - 4
  8. 21−4(3f−2)=f−1221 - 4(3f - 2) = f - 12

15) Vyřeš dané rovnice:

  1. 9(2x−3)+7=4(5x+1)−159(2x - 3) + 7 = 4(5x + 1) - 15
  2. 4(4y+1)−17=3(5y−2)+64(4y + 1) - 17 = 3(5y - 2) + 6
  3. 19a−5(2a−3)=2(a+9)−119a - 5(2a - 3) = 2(a + 9) - 1
  4. 6(3b−4)+11=5(2b+3)−86(3b - 4) + 11 = 5(2b + 3) - 8
  5. 24c−2(6c−5)=3(c−8)+724c - 2(6c - 5) = 3(c - 8) + 7
  6. 31−3(4d+2)=2d+1331 - 3(4d + 2) = 2d + 13
  7. 7(3e−5)+18=4(5e+1)−97(3e - 5) + 18 = 4(5e + 1) - 9
  8. 27−5(2f−3)=f−1427 - 5(2f - 3) = f - 14
  9. 2(8g+1)−21=3(4g−5)+22(8g + 1) - 21 = 3(4g - 5) + 2
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