Question

How do you solve `\frac { x } { 4} + \frac { 2} { 5} = \frac { x } { 2} - 1`?

Answer 1

`x=28/5`

Explanation:

We need to change the denominators so that they are they the same.
`x/4+2/5=x/2-1`
Let's make the denominator for all the fractions `20`:
`5/5xx x/4+2/5xx4/4=10/10xx x/2-20/20`

`(5x)/(20)+(8)/(20)=(10x)/(20)-20/20`

`(5x+8)/20=(10x-20)/20`

multiply by `20` on both sides

`5x+8=10x-20`

subtract `8`

`5x=10x-28`

subtract `10x`

`-5x=-28`

divide by `-5`

`x=28/5`

Answer 2

`x=28/5`

Explanation:

One way is to collect the terms in x on the left side and numeric values on the left side.

`"add 1 to both sides and subtract " x/4" from both sides"`

`rArr2/5+1=x/2-x/4`

`rArr7/5=x/4`

`color(blue)"cross-multiplying " "gives"`

`5x=28`

`"divide both sides by 5"`

`(cancel(5) x)/cancel(5)=28/5`

`rArrx=28/5`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution

`(28/5)/4+2/5=28/20+8/20=36/20=9/5larrcolor(red)" left side"`

`(28/5)/2-1=28/10-10/10=18/10=9/5larrcolor(red)" right side"`

`rArrx=28/5" is the solution"`