Question

How do you solve `2/3x + 4 = 3/5x - 2`?

Answer 1

`x = -90`

Explanation:

Given: `2/3x + 4 = 3/5x - 2`

One way to solve this equation is to multiply the whole equation by the common denominator of the two fractions to eliminate fractions:

The least common multiple (LCM) or common denominator of `3 " & "5`:

`" "3: 3, 6, 9, 12, color(red)(15), 18`

`" "5: 5, 10, color(red)(15), 20`

`15/1 xx (2/3x + 4 = 3/5x - 2)`

`30/3 x + 60 = 45/5x - 30; " " 10x + 60 = 9x - 30`

Move the `x's` to the same side:

`" "10x + 60 = " "9x - 30`
`ul(+" "-9x " " = -9x " ")`
`" "x + 60 = " "-30`
`ul(" " -60 = " "-60`
`" "x = -90`

Check:
`2/3 xx (-90/1) + 4 = 3/5 xx (-90/1) - 2`

`-180/3 + 4 = -270/5 - 2`

`-60+4 = -54 - 2`

`-56 = -56` QED