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Question

(1) If the sum of a number and two is doubled, the result is six less than three times the number. Find the number.
(2)Four times the difference of a number and one is equal to six times the sum of the number and three. Find the number.
(3)Five times a number, added to 6, is 16. Find the number.
(4) Six times a number, added to -63, is -105. Find the number.
(5)Three times the sum of some number plus 2 is equal to 6 times the number minus 21.
(6)The difference of a number and 9 is the same as 39 less the number. Find the number.
(7) Five times some number added to 8 amounts to 22 added to the product of 3 and the number.
(8) Twice the sum of a number and -8 gives 18. Find the number.

Answer 1

1) Let required number  =x

Sum of the number and two is doubled is be 2(2+x)

Six less than three times the number is be 3x-6

According to given problem 2(2+x) = 3x-6

4+2x = 3x-6

4+2x-3x+6 = 0

-x+10 = 0

x = 10

Required number = 10

2) Required number = x

Four times the difference of the number and one is be 4(x-1)

Six times the sum of the number and three is be 6(x+3)

According to the given problem 4(x-1) = 6(x+3)

4x-4 = 6x+18

4x-4-6x-18 = 0

-2x-22 = 0

-2x = 22

x = 22/-2

x = -11

Required number = -11

3)Required number = x

Five times of the number added to 6 is be 5x+6

According to given problem 5x+6 = 16

5x = 16-6

5x = 10

x = 10/5

x = 2

Required number = 2

4)Required number = x

Six times of numer added to-63 is be 6x-63

According to given problem 6x-63 = -105

6x = -105+63

6x = -42

x = -42/6

x = -7

Required number = -7

 

Answer 2

5) Let required number = x

Three times the sum of the number  plus 2 is equal to 6 times the number minus 21.

It's algebraic expression is 3(x + 2) = 6x - 21

3x + 6 = 6x - 21

6x - 3x = 6 + 21

3x = 27

x = 27/3

x = 9

Thefore, the number is 9.

6) Let required number = x

The difference of the number and 9 is same as 39 less than the number.

It's algebraic expression is 9 - x = x - 39

x + x  = 9 + 39

2x = 48

x = 48/2

x = 24

Thefore, the number is 24.

7) Let required number = x

Five times of the number added to 8 is equal to 22 added to the product of 3 and the number.

It's algebraic expression is 5x + 8 = 22 + 3x

5x - 3x = 22 - 8

2x = 14

x = 14/2

x = 7

Thefore, the number is 7.

8) Let required number = x

Twice the sum of the number and - 8 equals to 18.

It's algebraic expression is 2(x - 8) = 18

2x - 16 = 18

2x = 18 + 16

x = 34/2

x = 17

Thefore, the number is 17.