SOLVING LINEAR EQUATIONS WITH FRACTIONAL COEFFICIENTS

Solve each equation.

Problem 1 :

m + 4 = 13/2

Solution :

m + 4 = 13/2

Subtract 4 from each side.

m + 4 - 4 = (13/2) – 4

m = (13 – 8)/2

m = 5/2

Problem 2 :

8/3 = x – 1 1/3

Solution :

8/3 = x – 1 1/3

8/3 = x – 4/3

Adding 4/3 on both side.

8/3 + 4/3 = 4/3 + x – 4/3

12/3 = x

4 = x

Problem 3 :

4/5 + v = 41/20

Solution :

4/5 + v = 41/20

Subtract  4/5 from each side.

4/5 + v – 4/5 = 41/20 – 4/5

v = 41/20 – 4/5 × (4/4)

v = 41/20 – 16/20

v = 25/20

v = 5/4

Problem 4 :

-11/5 = -2 + n

Solution :

-11/5 = -2 + n

Adding 2 on each side.

-11/5 + 2 = -2 + n + 2

(-11 + 10)/5 = n

-1/5 = n

Problem 5 :

-17/4 = v - 2

Solution :

-17/4 = v - 2

Adding 2 on each side.

-17/4 + 2 = v – 2 + 2

(-17 + 8)/4 = v

-9/4 = v 

Problem 6 :

x + 1 = 11/5

Solution :

x + 1 = 11/5

Subtract 1 from each side.

x + 1 – 1 = 11/5 - 1

x = (11 – 5)/5

x = 6/5

Problem 7 :

(2/3)x = -1

Solution :

(2/3)x = -1

Multiplying both side by 3.

(2/3)x . 3 = -1.3

2x = -3

Divide each side by 2.

2x/2 = -3/2

x =-3/2

Problem 8 :

-3/2 = -3/2x

Solution :

-3/2 = (-3/2)x

Multiplying both side by 2.

(-3/2) . 2 = (-3/2) . 2

-3 = -3x

Divide each side by 3.

-3/3 = -3x/3

-1 = -x

x = 1

Problem 9 :

(2/5)x = -1/10

Solution :

(2/5)x = -1/10

Using cross multiplication.

20x = -5

Diving by 20

x = -1/4

Problem 10 :

-9/4 = -5x/4

Solution :

-9/4 = -5x/4

Multiplying both side by 4.

(-9/4) . 4 = (-5x/4) . 4

-9 = -5x

Divide each side by -5.

-9/(-5) = -5x/(-5)

9/5 = x