Question

How do you solve `\frac { 8( 6t - 22) } { 14} = \frac { 9( 10t - 18) } { 21}`?

Answer 1

`t=-17/3`

Explanation:

`(8(6t-22))/14=(9(10t-18))/21`

Let's use the distributive property to condese all our numbers:

`(48t-176)/14=(90t-162)/21`

Let's see if we can simplify the numerators and denominators by factoring out a common multiple:

`(cancel(2)(24t-88))/(cancel(2)xx7)=(cancel(3)(30t-54))/(cancel(3)xx7)`

`((24t-88))/(7)=((30t-54))/(7)`

multiply both sides by `7`

`cancel(7)*((24t-88))/(cancel(7))=((30t-54))/(cancel(7))*cancel(7)`

Now we're left with `24t-88=30t-54`

subtract `24t` on both sides

`-88=6x-54`

add `54` on both sides

`-34=6t`

divide by `6` on both sides

`t=-34/6`

expand and simplify

`t=(-1xx17xxcancel(2))/(3xxcancel(2))`

`t=-17/3`