Question

What is the value of x in the equation 4/7(21/8x+1/2)=-2(1/7-5/28x)? Write your solution in decimal form.

Answer 1

- 0.5

Explanation:

Given equation is,

`(4)/(7)((21)/(8)x+(1)/(2))=-2((1)/(7)-(5)/(28)x)`

By distributive property,

`(84)/(56)x+(4)/(14)=-(2)/(7)+(10)/(28)x`

Subtraction property of equality,

`(84)/(56)x-(10)/(28)x=-(2)/(7)-(4)/(14)`

Subtracting fractions,

`(84x-20x)/(56)=(-4-4)/(14)`

`(64x)/(56)=-(8)/(14)`

By cross multiplication,

`896x=-448`

By division property of equality,

`\implies x=-(448)/(896)=-0.5`

Answer 2

To solve this problem you must apply the proccedure shown below:

1. You have the following expression given in the problem above:

`(4)/(7) ((21)/(8x) +(1)/(2))=-2((1)/(7)-(5)/(28x))`

2. When you apply the distributive property, you obtain:

`(84)/(56x)+(4)/(14) =-(2)/(7)+(10)/(28x)`

3. When you order the terms and you sum the fractions, you have:

`(84)/(56x) -(10)/(28x) =-(2)/(7) -(4)/(14) \\ ((84-20))/(56x) =-(4)/(7) \\ (64)/(56x) =-(4)/(7)`

4. Now, solve for
`x`:

`x=(448)/(-224)\\x=-2.0`

The answer is:
`x=-2.0`