Question

How do you solve `-\frac { 2} { 3} q + 2q = \frac { 6} { 5} q + \frac { 6} { 5}`?

Answer 1

`q=9`

Explanation:

`-2/3xxq+2q=6/5xxq+6/5`

`4/3xxq=6/5xxq+6/5`

`4/3xxq-6/5xxq=6/5`

`2/15xxq=6/5`

`q=6/5xx15/2`

`q=9`

Answer 2

`q=9`

Explanation:

If you make all the denominators the same you can then just look at the numerators to solve this.

`color(white)("ddd")-(2q)/3color(white)("dd")+color(white)("ddd")2qcolor(white)("dddd")=color(white)("dd")(6q)/5color(white)("ddd")color(white)("dd")+6/5`

`-[(2qxx5)/(3xx5)]+[(2qxx15)/(1xx15)]=[(6qxx3)/(5xx3)]+[(6xx3)/(5xx3)]`

`color(white)("dddd")-(10q)/15color(white)("dd")+color(white)("ddd")(30q)/15color(white)("dd")=color(white)("ddd")(18q)/15color(white)("d")+color(white)("d")18/15`

The purist would now say: "Multiply both sides by 15"

`-10q+30q=18q+18`

subtract `18q` from both sides

`-10q+30q-18a=18`

`2q=18`

Divide both sides by 2

`q=18/2`

`q=(18-:2)/(2-:2) = 9/1=9`

Answer 3

`color(magenta)(q=9`

Explanation:

`-2/3q+2q=6/5q+6/5`

multiply both sides by`3`

`:.-2q+6q=18/5q+18/5`

multiply both sides by`5`

`:.-10q+30q=18q+18`

`:.20q=18q+18`

`:.20q-18q=18`

`:.2q=18`

`:.color(magenta)(q=9`

~~~~~~~~~~~~~~~~~~

check:-

substitute `color(magenta)(q=9`

`-2/3(color(magenta)9)+2(color(magenta)9)=6/5(color(magenta)9)+6/5`

`:.-18/3+18=54/5+6/5`

multiply both sides by`3`

`:.-18+54=162/5+18/5`

multiply bothd sides by`5`

`:.-90+270=162+18`

`:.color(magenta)(180=180`