Question

How do you solve `-\frac { 7} { 3} x - \frac { 7} { 6} = \frac { 4} { 3} x`?

Answer 1

`x=-7/22`

Explanation:

`"Note that " -7/3x=-(7x)/3`

To eliminate the fractions from the equation multiply ALL terms by the `color(blue)"lowest common multiple"` ( LCM ) of 3 and 6, the denominators of the fractions.

The LCM of 3 and 6 is 6

`(cancel(6)^2xx-(7x)/cancel(3)^1)+(cancel(6)^1xx-7/cancel(6)^1)=cancel(6)^2xx(4x)/cancel(3)^1`

`rArr-14x-7=8xlarrcolor(red)" no fractions"`

Collect terms in x on the left side and numeric values on the right side.

subtract 8x from both sides.

`-14x-8x-7=cancel(8x)cancel(-8x)`

`rArr-22x-7=0`

add 7 to both sides.

`-22xcancel(-7)cancel(+7)=0+7`

`rArr-22x=7`

divide both sides by - 22

`(cancel(-22) x)/cancel(-22)=7/(-22)`

`rArrx=-7/22`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side equals the right side then it is the solution.

`(-7/3xx-7/22)-7/6=49/66-77/66=-14/33larr" left"`

`"right side "=4/3xx-7/22=-14/33=" left side"`

`rArrx=-7/22" is the solution"`