Question

How do you solve `2/3(x-7)=4/5`?

Answer 1

The solution is `x=41/5`.

Explanation:

We can first apply the multiplication on the left side of the `=`

`2/3(x-7)=4/5`

`2/3*x-2/3*7=4/5`

We can continue calculating `2/3*7=14/3`

`2/3x-2/3*7=4/5`

`2/3x-14/3=4/5`

Now we want to isolate the term with the `x` and to do this we can add on both sides `14/3` in this way we can cancel the `-14/3` from the side where there is the term with the `x`

`2/3x-cancel(14/3)+cancel(14/3)=4/5+14/3`

`2/3x=4/5+14/3`

On the right side we can calculate `4/5+14/3`

`2/3x=4/5+14/3`

`2/3x=(3*4+14*5)/(3*5)`

`2/3x=(12+70)/(15)`

`2/3x=82/15`.

Finally we want to remove the coefficient in front of the `x`. We have that `x` is multiplied by `2` and divided by `3`, so we will divide by `2` and multiply by `3` both side of the equation

`2/3x=82/15`

`cancel(2/3)*cancel(3/2)x=82/15*3/2`

`x=82/15*3/2`

we can simplify `82/2=41` and `3/15=1/5`

`x=82/15*3/2=41/5`.

Answer 2

`x = (41) / (5)`

Explanation:

We have: `(2) / (3) (x - 7) = (4) / (5)`

Let's cross-multiply:

`=> 10 (x - 7) = 12`

Then, let's divide both sides of the equation by `2`:

`=> 5 (x - 7) = 6`

`=> 5 x - 35 = 6`

Adding `35` to both sides:

`=> 5 x = 41`

Finally, let's solve for `x` by dividing both sides by `5`:

`=> x = (41) / (5)`