Question

Solve the equation.
x-2/5=2/3-3x-2/6

Answer 1

11/48

Explanation:

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

collect like terms

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

taking LCM on both sides

[(x-2) + 5(3x)]/5 = [2(2) -2]/6

(16x - 2)/5 = 2/6

cross multiply

6(16x - 2) = 5(2)

96x - 12 = 10

96x = 22

therefore; X = 22/96

= 11/48

CHECK:

(11/48 - 2)/5 = 2/3 - 3(11/48) - 2/6

(-85/48)/5 = 2/3 - 11/16 - 2/6

-85/48 × ⅕ = -17/48

-17/48 = -17/48

Answer 2

`x=(11)/(60)`

Explanation:

Given the equation

`x-(2)/(5)=(2)/(3)-3x-(2)/(6)`

Lets solve for x.

Simplify the right side of the equation.

Cancel the common factor of 2 and 6 .

Factor 2 out of 2 .

`x-(2)/(5)=(2)/(3)-3x-(2(1))/(2(3))`

`x-(2)/(5)=(2)/(3)-3x-(1)/(3)`

Combine the numerators over the common denominator.

`x-(2)/(5)=-3x-(2-1)/(3)`

`x-(2)/(5)=-3x-(1)/(3)`

Move all terms containing x to the left side of the equation.

Add
`3x` to both sides of the equation.

`x-(2)/(5)+3x=(1)/(3)`

Add
`x` and
`3x`.

`4x-(2)/(5)=(1)/(3)`

Move all terms not containing x to the right side of the equation.

Add
`(2)/(5)` to both sides of the equation.

`4x=(1)/(3)+(2)/(5)`

To write
`(1)/(3)` as a fraction with a common denominator, multiply by
`(5)/(5)` .

`4x=(1)/(3)*(5)/(5) +(2)/(5)`

To write
`(2)/(5)` as a fraction with a common denominator, multiply by
`(3)/(3)`

`4x=(1)/(3)*(5)/(5) +(2)/(5)*(3)/(3)`

Simplify.

Write each expression with a common denominator of 15 , by multiplying each by an appropriate factor of 1 .

`4x=(11)/(15)`

Divide each term in
`4x=(11)/(15)` by 4 and simplify.

`x=(11)/(60)`