Question

How do you solve `2.5(x-3)+1.7x=10.8(x+1.5)`?

Answer 1

See entire solution process below:

Explanation:

First step is to expand the terms in parenthesis:

`color(red)(2.5)(x - 3) + 1.7x = color(blue)(10.8)(x + 1.5)`

`(color(red)(2.5) xx x) - (color(red)(2.5) xx 3) + 1.7x = (color(blue)(10.8) xx x) + (color(blue)(10.8) xx 1.5)`

`2.5x - 7.5 + 1.7x = 10.8x + 16.2`

Now group and combine like terms:

`2.5x + 1.7x - 7.5 = 10.8x + 16.2`

`4.2x - 7.5 = 10.8x + 16.2`

Next, we subtract the necessary terms to 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:

`4.2x - 7.5 - color(red)(4.2x) - color(blue)(16.2) = 10.8x + 16.2 - color(red)(4.2x) - color(blue)(16.2)`

`4.2x - color(red)(4.2x) - 7.5 - color(blue)(16.2) = 10.8x - color(red)(4.2x) + 16.2 - color(blue)(16.2)`

`0 - 7.5 - color(blue)(16.2) = 10.8x - color(red)(4.2x) + 0`

`-23.7 = 6.6x`

Now, we can divide each side of the equation by `color(red)(6.6)` to solve for `x` while keeping the equation balanced:

`-23.7/color(red)(6.6) = (6.6x)/color(red)(6.6)`

`-3.59 = (color(red)(cancel(color(black)(6.6)))x)/cancel(color(red)(6.6))`

`-3.59 = x`

`x = -3.59` rounded to the nearest hundredth