Question

How do you solve `3.56x+2.43=6.17x-11.40`?

Answer 1

`x = 13.83/2.61`

or

`x = 5.30` rounded to the nearest one-hundredth

Explanation:

First, isolate the `x` terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

`3.56x + 2.43 color(red)( - 3.56x + 11.40) = 6.17x - 11.40 color(red)( - 3.56x + 11.40)`

`3.56x - 3.56x + 2.43 + 11.40 = 6.17x - 3.56x - 11.40 + 11.40`

`0 + 2.43 + 11.40 = 6.17x - 3.56x - 0`

`2.43 + 11.40 = 6.17x - 3.56x`

`13.83 = (6.17 - 3.56)x`

`13.83 = 2.61x`

Now we can solve for `x` while keeping the equation balanced:

`13.83/color(red)(2.61) = (2.61x)/color(red)(2.61)`

`13.83/2.61 = (color(red)(cancel(color(black)(2.61)))x)/color(red)(cancel(color(black)(2.61)))`

`x = 13.83/2.61`