Question

How do you solve `3.5(x-5.6)+0.03x=4.2x-25.5`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`(3.5 xx x) - (3.5 xx 5.6) + 0.03x = 4.2x - 25.5`

`3.5x - 19.6 + 0.03x = 4.2x - 25.5`

Next, we can group and combine like terms on the left side of the equation:

`3.5x + 0.03x - 19.6 = 4.2x - 25.5`

`(3.5 + 0.03)x - 19.6 = 4.2x - 25.5`

`3.53x - 19.6 = 4.2x - 25.5`

Then, subtract `color(red)(3.53x)` and add `color(blue)(25.5)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`3.53x - 19.6 - color(red)(3.53x) + color(blue)(25.5) = 4.2x - 25.5 - color(red)(3.53x) + color(blue)(25.5)`

`3.53x - color(red)(3.53x) - 19.6 + color(blue)(25.5) = 4.2x - color(red)(3.53x) - 25.5 + color(blue)(25.5)`

`0 + 5.9 = (4.2 - color(red)(3.53))x - 0`

`5.9 = 0.67x`

Now, divide each side of the equation by `color(red)(0.67)` to solve for `x` while keeping the equation balanced:

`5.9/color(red)(0.67) = (0.67x)/color(red)(0.67)`

`8.806 = (color(red)(cancel(color(black)(0.67)))x)/cancel(color(red)(0.67))`

`8.806 = x`

`x = 8.806` rounded to the nearest thousandth.