Class 7 Mathematics Exercise 7.1 Full Solution

(1) Solution:- 4x+1 = 2x+7

=> 4x-2x = 7-1

=> x= 6/2

= 3

(2) Solution:- 5x-3 = 2x+3

=> 5x-2x = 3+3

=> x = 6/3

= 2

(3) Solution:- 3y+1 = 7y-1

=> 3y-7y= -1-1

=> – 4y = -2

=> y= 2/4

= ½

(4) Solution:- 7y-5 = y-1

=> 7y-y = -1 +5

=> y= 4/6

= 2/3

(5) Solution:- 17-2z = 3z+2

=> -2z-3z = 2-17

=> – 5z = -15

=> z = 15/5

= 3

(6) Solution:- 13z-5 = 3-2z

=> 13z +2z = 3+5

=> z =8/15

(7) Solution:- x/4 = 1/3

=> x= 4/3

(8) Solution:- x/2+1= 3

=> x/2 = 3-1

=> x= 4

(9) Solution:- x/3+5 = x/2+7

=> x/3 – x/2 = 7-5

=> 2x-3x/6 = 2

=> -x= 12

=> x= -12

(10) Solution:- y/2 – y/3 = y/5 – 1/6

=> y/2 – y/3- y/5 = -1/6

=> 15y-10y-6y/30 = -1/6

=> -y/30 = -1/6

=> y = 30/6

=> y = 5

(11) Solution:- y/5- 2/7 = 5y/7 – 4/5

=> y/5 – 5y/7 = -4/5+27

=> 7y-25y/35 = 10-28/35

=> -18y/35 = -18/35

=> y= 18/18

=1

(12) Solution:- 2x-1/3 = 5

=> 2x-1 = 15

=> 2x= 15+1

=> x= 16/2

= 8

(13) Solution:- 5x/7 + 4/5 = x/5+ 2/7

=> 5x/7 – x/5 = 2/7-4/5

=> 25x-7x/35 = 10-28/35

=> 18x/35= -18/35

Therefore, x= -18/18

= -1

(14) Solution:- y-2/4 +2y-1/3 = y- 1/3

=> y-2/4 + 1/3 = y – 2y-1/3

=> 3(y-2) +4= 12y-4 (2y-1) [Both side x by 12]

=> 3y-6 + 4= 12y – 8y +4

=> 3y-12y+8y= 4+6-4

=> -y= 6

=> y= -6

(15) Solution:- 3y+1/5 = 3y-7/3

=> 15y-35 = 9y +3

=> 15y-9y= 3+35

=> 6y= 38

=> y= 38/6

= 19/3

(16) Solution:- x +1/2 – x-2/3 – x-3/5 = 2

=> 15x +15 – 10x +20 – 6x +18/30 = 2

=> -x +53/30 = 2

=> -x +53 = 60

=> -x = 60- 53

=> x= -7

(17) Solution:- 2(x+3) = 10

=>2x +6=10

=> x= 4/2

= 2

(18) Solution:- 5(x-2) = (x-4)

=> 5x-10 = 3x-12

=> 5x-3x = -12+10

=> 2x= -2

=> x = -2/2

= -1

(19) Solution:- 7(3-2y) + 5(y-1) = 34

=> 21-14y+5y-5 = 34

=> -9y = 34-21+5

=> -y= 18/9

=> y= -2

(20) Solution:- (z-1) (z+2) = (z+4) (z-2)

=> z²+2- z-2= z2-2z-2z+4z-8

=> z²+z-2= z²+2z-8

=> z²+z-z²= -8+2

=> -z= 6

Therefore, z= 6