Question

Solve. 

A. 4y- 4 + y = 6y + 20 - 4y 

B. -3.7x + 6.2 = -7.3x -5.8

C. -3(x - 2) = -15

D. 1/3x - 5/6 = 1/2 +2 

Answer 1

A) The equation is 4y - 4 + y = 6y + 20 - 4y

Separate the variables and constants in above equation.

4y + y - 6y + 4y = 20 + 4

Combine like terms.

3y = 24

Divide each side by 3.

3y/3 = 24/3

3y/3 = (8*3)/3

Cancel common terms.

y = 8

The solution is y = 8.

B) The equation is - 3.7x + 6.2 = - 7.3x - 5.8

Separate the variables and constants in above equation.

- 3.7x + 7.3x = - 5.8 - 6.2

Combine like terms.

3.6x  = -12

Divide each side by 3.6.

3.6x/3.6 = -12/3.6

1*x = -3.33

Apply identity property of multiplication: 1*a = a.

The solution is x = -3.33.

C) The equation is - 3(x - 2) = - 15 and solve for x as follows :

Apply distributive property : a(b - c) = ab - ac.

(- 3)(x) - (- 3)(2) = - 15

- 3x + 6 = - 15

Subtract 6 from each side.

- 3x + 6 - 6 = - 15 - 6

- 3x = - 21

Divide each side by negative 3.

(- 3x) / (- 3) = (- 3*7) / (- 3)

Cancel common terms.

x = 7.

The solution of x = 7.

 

Answer 2

D) The equation is 1/3 x - 5/6 = 1/2 + 2 and solve for x as follows :

Add 5/6 to each side.

1/3 x - 5/6 + 5/6 = 1/2 + 2 + 5/6

1/3 x = 1/2 + 2 + 5/6

Fractions with different denominators can not be added. So, write the equation with common denominator.

Find the least common denominator L.C.M.

Multiples of 2 = 2, 4, 6, 8

Multiples of 1 =1, 2, 3, 4, 5, 6 , 7

Multiples of 6 = 6,12,18, 24

Least Common Multiple of 2, 1 and 6 is 6.

Write the right hand side equation with common denominator.

1/3 x = (1/2)*(3/3) + 2*(6/6) + (5/6)*(1/1)

1/3 x = 3/6 + 12/6 + 5/6

1/3 x = (3 + 12 + 5)/6

1/3 x = 20/6

1/3 x = 10/3

Multiply each side by 3.

x = 10

The solution of x = 10.