Question

Question #92f49

Answer 1

`1 13/84` or `97/84`

Explanation:

`x-7/12=4/7`
First, we add `7/12` to both sides, so instead of the equation being `x-7/12`, we can make it just `x`.
So when you add `7/12` to both sides, it will look like this.
`x-7/12color(blue)+color(blue)7color(blue)/color(blue)12=4/7color(blue)+color(blue)7color(blue)/color(blue)12`
That means
`x=4/7+7/12`.
To do `4/7+7/12` We find the least common denominator.
`7*12=84`
Then we adjust fractions based on the least common denominator (84).

`(4*12)/84+(7*7)/84`

Since the denominators are equal, combine the fractions.

`(4*12+7*7)/84`

`4*12=48` and `7*7=49`
`49+48=97`
Ans: #97/84

To change to a mixed number.
97 has one group of 84 and 13 remaining so it will be `1 13/84`.

Ans: `97/84` or `1 13/84`.

Answer 2

If you meant: `(x-7)/12=-4/7,` `x=1/7`

If you meant: `x-7/12=-4/7,` `x=1/84`

Explanation:

`color(green)"If you meant":` `(x-7)/12=-4/7`.

Solve:

`(x-7)/12=-4/7`

Multiply both sides of the equation by `12`.

`12xx(x-7)/12=-4/7xx12`

Simplify.

`color(red)cancel(color(black)(12))^1xx(x-7)/color(red)cancel(color(black)(12))^1=-4/7xx12`

`x-7=-48/7`

Add `7` to both sides of the equation.

`x-7+7=-48/7+7`

Simplify.

`x=-48/7+7`

For any whole number, `n=n/1`.

Rewrite the equation.

`x=-48/7+7/1`

In order to add or subtract fractions, they must have the same denominator, called the least common denominator, or LCD. We can multiply the denominators to get `7` as the LCD. Now we need to multiply `7/1` by a fraction equal to `1` that will give it the denominator `7`. An example is `5/5=1`.

`x=-48/7+7/1xxcolor(red)7/color(red)7`

Simplify.

`x=-48/7+49/7`

`x=1/7`

`color(blue)"If you meant:" color(white)(.) x-7/12=-4/7`.

Solve:

`x-7/12=-4/7`

Add `7/12` to both sides.

`x-7/12+7/12=-4/7+7/12`

Simplify.

`x=-4/7+7/12`

We need to find a common denominator in order to add the fractions. Multiply the denominators `7` and `12` to get `84`. Now multiply both fractions by a fraction that equals `1` and makes the denominator `84`. For example, `9/9=1`. This way the value of the fraction does not change, it just changes in appearance.

`x=-4/7xx12/12+7/12xx7/7`

Simplify.

`x=-48/84+49/84`

`x=(-48+49)/84`

`x=1/84`