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Home / Algebra / Solution of Simple equation

# Problem: 1. 4x + 1 = 2x + 7

Solution: 4x + 1 = 2x + 7

⇒ 4x – 2x = 7 – 1

⇒2x = 6

⇒ x = 3 [dividing by 2]

∴ required solution is 3.

Problem: 2. 5x – 3 = 2x + 3

Solution: 5x – 3 = 2x + 3

⇒5x – 2x = 3+3

⇒3x = 6

⇒ x = 2 [dividing by 3]

∴ required solution is 2

Problem- 3: 3y +1 = 7y-1

Solution: 3y +1 = 7y-1

⇒3y – 7y = -1-1

⇒ -4y = -2

⇒4y = 2    [multiplying by -1 on both side]

⇒y = ½     [dividing by 2]

∴ required solution is ½.

Problem-4: 7y – 5 = y-1

Solution: 7y – 5 = y-1

⇒7y-y=-1+5 [by transposing]

⇒6y =4

⇒y = 4/6

⇒y = 2/3

∴ required solution is 2/3.

Problem-5: 17 -2z=3z+2

Solution: 17 -2z=3z+2

⇒-2z-3z=2-17 [by transposing]

⇒-5z=-15

⇒5z =15             [multiplying by -1]

⇒z=3

∴ required solution is 3

Problem-6: 13z-5 =3-2z

Solution: 13z-5 =3-2z

⇒13z+2z=3+5

⇒15z =8

⇒z = 8/15

∴ required solution is 8/15

Problem-7. 2 ( x + 3) = 10

Solution: 2 ( x + 3) = 10

⇒ 2x + 6 = 10

⇒ 2x = 10 – 6

⇒ 2x = 4

⇒ x = 2 [by dividing 2]

∴ required solution = 2 (Answer)

Problem-8. 5(x – 2) = 3(x – 4)

Solution: 5(x – 2) = 3(x – 4)

⇒ 5x – 10 = 3x – 12

⇒ 5x – 3x = – 12 + 10

⇒ 2x = – 2

⇒ x = – 1 [by dividing 2]

∴ required solution = – 1 (Answer)

Problem-9. 7(3 – 2y) + 5(y – 1) = 34

Solution: 7(3 – 2y) + 5(y – 1) = 34

⇒ 21 – 14y + 5y – 5 = 34

⇒ 16 – 9y = 34

⇒ – 9y = 34 – 16

⇒ – 9y = 18

⇒ y = – 2 [by dividing – 9]

∴ required solution = – 2 (Answer)

Problem-10. (z – 1) (z + 2) = (z + 4) (z – 2)

Solution: (z – 1) (z + 2) = (z + 4) (z – 2)

⇒ z2 + 2z – z – 2 = z2 – 2z + 4z – 8

⇒ z2 + 2z – z – 2 – z2 + 2z –  4z = 2– 8

⇒ 4z – 5z = – 6

⇒ – z = – 6

⇒ z = 6 [multiplying by –1]

∴ required solution = 6 (Answer)

Problem-11. 4x + 3 = 2x + 5

Solution: 4x + 3 = 2x + 5

⇒ 4x – 2x = 5 – 3

⇒ 2x = 2

⇒ x = 1

∴ required solution = 1 (Answer)

Problem-12. 3x + 2 = x + 6

Solution: 3x + 2 = x + 6

⇒ 3x – x = 6 – 2

⇒ 2x = 4

⇒ x = 2

∴ required solution = 2 (Answer)

Problem-13. 5x – 6 = 2x + 3

Solution: 5x – 6 = 2x + 3

⇒ 5x – 2x = 6 + 3

⇒ 3x = 9

⇒ x = 3 [by dividing 3]

Problem-14. 15 x – 9 = 11x – 25

Solution: 15 x – 9 = 11x – 25

⇒ 15x – 11x = 9 – 25

⇒ 4x = – 16

⇒ x = – 4

∴ required solution = – 4 (Answer)

Problem-15. 19 – 3x = 5x + 35

Solution: 19 – 3x = 5x + 35

⇒ – 3x – 5x = 35 – 19

⇒ – 8x = 16

⇒ x = – 2

∴ required solution = – 2(Answer)

Problem-16. 2x + 9 = 13x – 17

Solution: 2x + 9 = 13x – 17

⇒ 2x – 13x = – 9 – 17

⇒ – 11x = – 26

⇒ 11x = 26 [multiplying by – 1]

⇒ x = 26/11

∴ required solution = 26/ 11 (Answer)

Problem-17. 15x – 9 = 11x – 35

Solution: 17. 15x – 9 = 11x – 35

⇒ 15x – 11x = 9 – 35

⇒ 4x = – 26

⇒ x = – 26/4

∴ required solution = – 26/4

Problem-18. 4(2–x) + 2(3 – 2x) = 30

Solution: 4(2–x) + 2(3 – 2x) = 30

⇒ 8 – 4x + 6 – 4x = 30

⇒ 14 – 8x = 30

⇒ – 8x = 30 – 14

⇒ – 8x = 16

⇒ x = – 2 [dividing by –8]

Problem-19. 3(x – 2) + 7(2x – 3) = 5(1 – 2x) – 59

Solution: 3(x – 2) + 7(2x – 3) = 5(1 – 2x) – 59

⇒ 3x– 6 + 14x – 21 = 5 – 10x – 59

⇒ 17x – 27 = – 10x – 54

⇒ 17x + 10x = 27 – 54

⇒ 27x = – 27

⇒ x = – 1 [dividing by 27]

∴ required solution = 27 (Answer)

Problem-20. 8(2x –7) ­– 9(3x – 14) – 15 = 0

Solution: 8(2x –7) ­– 9(3x – 14) – 15 = 0

⇒ 16x ­– 56 – 27x + 126 – 15 = 0

⇒ – 11x + 126 – 71 = 0

⇒ –11x + 55 = 0

⇒ – 11x = – 55

⇒ x = 5

∴ required solution = 5 (Answer)

## Simple Equation Solution

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