Question

Question #2b76d

Answer 1

In this case, the set of like terms are `3/5x` and `7/8x`. To combine them, let's subtract `3/5x` from both sides. On the left side, the positive and negative `3/5x` cancel each other out or become equal to `0`.
`3/5x -(3/5x + 33 = 7/8x)- 3/5x`

So this is how our solution looks like.
`33 = 7/8x - 3/5x`

Let's focus on those two fractions. We'll be subtracting dissimilar fractions. First, we find the LCD (Least Common Denominator) of `8` and `5`, which is `40`.
`7/8x - 3/5x = -/40`

Next, we divide `40` by `8` and `5`. Then, the quotient of `40` and `8` is `5` and will be multiplied to `7`. The quotient of `40` and `5` is `8` and will be multiplied by `3`. The solution looks like this:
`7/8x - 3/5x = (35-24)/40`

Subtract 35 and 24 to get the following:
`33 = 11/40x`

Now let's isolate the variable `x`. We could apply cross-multiplication by multiplying `33` by `40`, `11` by `1` (which is underneath `33` this whole time). Solution becomes like this:
`33/1 = 11/40x` ==> `1320 = 11x`

DIvide both sides by `11` to get `x = 120`.
`1320/11 = 11/11x` ==> `120 = x`

Answer 2

`x = 120`

Explanation:

`3/"5" .x + 33 = 7/"8".x`

Now, subtracting `3/"5".x` from the both sides

`cancel(3/"5".x) + 33 -cancel( 3/"5".x) = 7/"8".x - 3/"5".x`

`33 = x. (7/"8" - 3/"5")`

`33 = x. ("7(5) - 3(8)"/"40")`

`33 = x. ("35 - 24"/"40")`

`33 = x. 11/"40"`

Multiplying the both sides by 40
`33 × 40 = x. 11/cancel("40" )× cancel(40)`

`33 × 40 = x. 11`

Now, dividing the both sides by 11

`cancel"(33)"^3 × 40/cancel"(11)" = x. cancel"(11)"/cancel"(11)"`

`3 × 40 = x`

`120 = x`