Question

How do you solve `\frac { 6} { x + 4} + \frac { 1} { 8} = \frac { 7} { 8}`?

Answer 1

We start by subtracting `1/8` on both sides:

Explanation:

`6/(x+4)+cancel(1/8)-cancel(1/8)=7/8-1/8->`

`6/(x+4)=6/8`

Now we can divide both sides by `6`:
`1/(x+4)=1/8->x+4=8->x=4`

Check with the original equation:
`6/(4+4)+1/8=7/8->6/8+1/8=7/8`

Answer 2

`x=4`

Explanation:

Collect numeric values on the right side of the equation.

subtract `1/8" from both sides"`

`6/(x+4)cancel(+1/8)cancel(-1/8)=7/8-1/8`

`rArr6/(x+4)=6/8=3/4`

`rArrcolor(blue)(6)/color(red)(x+4)=color(red)(3)/color(blue)(4)`

To solve this fractional equation we can use the method of `color(blue)"cross-multiplication".` That is multiply the `color(blue)"blue terms"` together, the `color(red)"red terms "`together and equate them.

`color(red)(3(x+4))=color(blue)(6)xxcolor(blue)(4)`

`rArr3(x+4)=24`

distribute the bracket.

`3x+12=24`

subtract 12 from both sides.

`3xcancel(+12)cancel(-12)=24-12`

`rArr3x=12`

To solve for x, divide both sides by 3

`(cancel(3) x)/cancel(3)=12/3`

`rArrx=4" is the solution"`

Answer 3

`x=4`

Explanation:

`6/(x+4)+1/8=7/8`

`6/(x+4)=6/8`

cross multiply:

`6(x+4)=48`

`6x+24=48`

`6x=48-24`

`6x=24`

`x=4`

substitute x=4

`6/(4+4)+1/8=7/8`

`6/8+1/8=7/8`

`7/8=7/8`

Answer 4

`x=4`

Explanation:

Very often in our desire to do maths, we miss the most obvious and the simplest approach. This is just such a case.

`6/(x+4) +1/8 = 7/8" "` subtract `1/8` from each side

`color(blue)(6)/color(red)((x+4)) = color(blue)(6)/color(red)8`

If you now just LOOK at the two equivalent fractions, we can see the the numerators are equal. (`color(blue)(6 = 6)`)

Therefore it follows that the denominators must be equal...

`color(red)(x+4 =8)`

`x=4`