Question

How do you solve `9.2- 1.7x = 2.3x + 1.2`?

Answer 1

`color(green)(x=2)`

Explanation:

Given
`color(white)("XXX")9.2-1.7x=2.3x+1.2`

Multiply everything on both sides by `10` to get rid of the fractions.
(This is not technically necessary, but I personally find it easier to work with integers when possible).
`color(white)("XXX")92-17x=23x+12`

Add `17x` to both sides
`color(white)("XXX")92=40x+12`

Subtract `12` from both sides
`color(white)("XXX")80=40x`

Divide both sides by `40`
`color(white)("XXX")2=xcolor(white)("XX")` or equivalently`color(white)("XX")x=2`

Answer 2

`x=1.75=7/4`

Explanation:

Collect terms in x to one side of the equation and numeric values to the other side.

add 1.7x to both sides.

`9.2cancel(-1.7x)cancel(+1.7x)=2.3x+1.7x+1.2`

`rArr9.2=4x+1.2`

subtract 1.2 from both sides.

`9.2-1.2=4xcancel(+1.2)cancel(-1.2)`

`rArr7=4x`

To solve for x, divide both sides by 4.

`7/4=(cancel(4) x)/cancel(4)`

`rArrx=7/4=1.75" is the solution"`