Question

-4/5 x + 2/3 = 1 and 3/4x +2 What is x?

Answer 1

`x=–80/153`.

Explanation:

This question is similar to one asked previously. It is possible to interpret it as

`–4/5x+2/3=1 3/4x+2`

Step 1: Turn proper fractions into improper ones. They are easier to work with in equations. (If our answer ends up being an improper fraction, we can always rewrite it as a proper one at the end.)

`–4/5x+2/3=7/4x+2`

Step 2: Multiply through by a common multiple of all denominators. Here those are 5, 3, and 4. The least common multiple of these is 60.

`–48x+40=105x+120`

Step 3: Move all terms with `x` to the left side; move all terms without `x` to the other side.

`–48x-105x=120-40`

Step 4: Combine like terms.

`–153x=80`

Step 5: Isolate `x` by dividing both sides by its coefficient.

`x=–80/153`

Since 80 and 153 share no common factors, this is our final answer.