Question

How do you solve `-8-\frac{2}{5}x=\frac{1}{2}(x-7)`?

Answer 1

`x=-5`

Explanation:

`"multiply ALL terms by 10 to eliminate fractions"`
`"10 is the lowest common multiple of 5 and 2"`

`(-8xx10)-(cancel(10)^2xx(2x)/cancel(5)^1)=cancel(10)^5xx1/cancel(2)^1(x-7)`

`rArr-80-4x=5(x-7)larrcolor(blue)"no fractions"`

`rArr-80-4x=5x-35`

`"add 4x to both sides"`

`-80cancel(-4x)cancel(+4x)=5x+4x-35`

`rArr-80=9x-35`

`"add 35 to both sides"`

`-80+35=9xcancel(-35)cancel(+35)`

`rArr9x=-45larrcolor(blue)"reversing the equation"`

`"divide both sides by 9"`

`(cancel(9) x)/cancel(9)=(-45)/9`

`rArrx=-5`

`color(blue)"As a check"`

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

`"left "=-8-2/5xx-5=-8+2=-6`

`"right "=1/2(-5-7)=1/2xx-12=-6`

`rArrx=-5" is the solution"`