Question

How do you solve `\frac{ 2}{ 5} x - \frac{ 1}{ 4} ( x - 8) = \frac{ 13}{ 2}`?

Answer 1

`x=30`

Explanation:

We can eliminate the fractions in the equation by multiplying ALL terms on both sides by the `color(blue)"lowest common multiple"` (LCM) of 5 , 4 and 2. The LCM is 20.

`"Note that" 2/5x=(2x)/5`

`(cancel(20)^4xx(2x)/cancel(5)^1)-(cancel(20)^5xx1/cancel(4)^1(x-8))=cancel(20)^(10)xx13/cancel(2)^1`

`rArr8x-5(x-8)=130`

distributing gives.

`8x-5x+40=130`

simplify left side by collecting like terms.

`rArr3x+40=130`

subtract 40 from both sides.

`3xcancel(+40)cancel(-40)=130-40`

`rArr3x=90`

To solve for x, divide both sides by 3

`(cancel(3) x)/cancel(3)=90/3`

`rArrx=30" is the solution"`

`color(blue)"As a check"`

`"left side "=2/5xx30-1/4(30-8)`

`=12-11/2=24/2-11/2=13/2="right side"`

Answer 2

`x=30`

Explanation:

`2/5x-1/4(x-8)=13/2`

`2/5x-x/4+2/1=13/2`

`(8x-5x+40)/20=13/2`

multiply both sides by 20

`8x-5x+40=260/2`

`3x=130-40`

3x=90##

`x=30`

substitute `x=30`

`8(30)-5(30)+40=260/2`

`240-150+40=130`

`130=130`