Algebra - Linear Equations

Solving Linear Equation 1

100

x + 8 = 15 

x = ?

x = 15 - 8

x = 7

200

-24x = -144 

x = ?

x = -144 : -24

x = 6

300

7(-2x + 4) = -4x 

x = ?

-14x + 28 = -4x 

-14 x + 4x = -28

-10x = -28

x = -28/-10 

x = 2 8/10 or 2 4/5 or 2.8 

400

-2.7 + a = -6.4 

a = ?

-2.7 + 6.4 = -a 

3.7 = -a 

a = 3.7/-1 

a = - 3.7 

500

-3(2 - x) = 6x

x = ?

-6 + 3x = 6x

 3x - 6x = 6 

-3x = 6 

x = 6/-3

x = -2

Solving Linear Equations with Fractional Coefficients 1

100

1/3 x = 7 

x = ?

1/3 x = 7 

x = 7 : 1/3 

x = 7 X 3/1 

x = 21

200

3 - 1/4 y = 2

y = ?

-1/4 y = 2 - 3 

-1/4 y = -1 

y = -1 : -1/4 

y = -1 x -4/1

y = 4

300

x = 12 - 1/3 x 

x = ?

x + 1/3 x = 12

4/3 x = 12 

x = 12 : 4/3 

x = 12 X 3/4 

x = 9

400

y/2 - 1/5 = 2 - y/3 

y = ?

y/2 + y/3 = 2 + 1/5 

3y/6 + 2y/6 = 10/5 + 1/5

5y/6 = 11/5 

y = 11/5 : 5/6

y = 11/5 X 6/5 

y = 66/25

y = 2 16/25

500

2/x = 4/5 

x = ?

2/x X x = 4/5 X x 

2 = 4/5 x 

x = 2 : 4/5 

x = 2 X 5/4 

x = 5/2

Solving Linear Equation 2

100

x + 9 = -5 

x = ?

x = -5 -9

x = -14

200

30 + 7y = - 2y - 6

y = ?

30 + 6 = - 2y - 7y 

36 = - 9y

y = 36 : -9 

y = -4

300

3 (2y + 3) = 4y +3 

y = ?

6y + 9 = 4y + 3 

6y - 4y = 3 - 9 

2y = -6 

y = -6/2 

y = -3 

400

2(2x - 2.2) = 4.6 

x = ?

4x - 4.4 = 4.6 

4x = 4.6 + 4.4 

4x = 9 

x = 9/4 

x = 2 1/4 or 2.25

500

3(5 - h) - 2(h - 2) = -1

h = ?

15 - 3h - 2h + 4 = -1

15 + 4 - 3h - 2h = -1

19 - 5h = -1 

-5h = -1 -19 

-5h = -20 

h = -20/-5

h = 4

Solving Linear Equations with Fractional Coefficients 2

100

3/4 x = -6 

x = ?

3/4 x = -6 

x = -6 : 3/4

x = -6 X 4/3 

x = -8

200

15 - 2/5 y = 11 

y = ?

-2/5 y = 11-15

-2/5 y = -4 

y = -4 : -2/5

y = -4 X -5/2

y = 10

300

3/5 x = 1/2 x + 1/2

x = ?

3/5 x  - 1/2 x = 1/2 

6/10 x - 5/10 x = 1/2 

1/10 x = 1/2 

x  = 1/2 : 1/10

x  = 1/2 X 10/1 

x = 5

400

2/3 y - 3/4 = 2y + 5/8 

y = ?

2/3y - 2y = 5/8 + 3/4 

2/3 y - 6/3 y = 5/8 + 6/8

-4/3 y = 11/8 

y = 11/8 : -4/3 

y = 11/8 X -3/4 

y = -33/32 

y = - 1 1/32

500

12/y-1 = 2/3 

y = ?

12/y-1 X y-1 = 2/3 X y-1 

12 = 2/3 y - 2/3 

12 + 2/3 = 2/3 y

36/3 + 2/3 = 2/3 y

38/3 = 2/3 y 

38/3 : 2/3 = y 

38/3 X 3/2 = y 

y = 19

Medium-Hard

100

By showing your working clearly. verify if x = 19/20 is the solution of the equation 2x - 3/4 = 1/3 x + 5/6.

Verified.

200

Solve this following equation.

2/y-2 = 3/y+6

2(y+6) = 3(y-2)

2y + 12 = 3y -6 

2y - 3y = -6 - 12

-y = -18 

y = 18

300

Solve this following equation. 

(2y + 1)/(3y - 5) = 4/7

7(2y + 1) = 4(3y - 5)

14y + 7 = 12y - 20

14y - 12y = -20 - 7 

2y = -27

y = -27/2 

y = - 13 1/2

400

If 4x + y = 3x + 5y, find the value of 3x/16y. 

4x - 3x = 5y - y 

x = 4y 

so, 3x/16y 

= [3(4y)]/16y

= 12y/16y

= 3/4

500

If (3x - 5y)/(7x-4y) = 3/4, find the value of x/y.

4(3x - 5y) = 3(7x - 4y)

12x - 20y = 21x - 12y 

12x - 21x = -12y + 20y 

-9x = 8y 

x = -8/9y 

so x/y 

= -8/9 y : y 

= -8/9