Question

How do you solve `(x - 1) - ( 2x - 3) = \frac { 5x - 3} { 3}`?

Answer 1

See a solution process below:

Explanation:

First, group and combine like terms on the left side of the equation:

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

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

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

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

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

`-x + 2 = (5x - 3)/3`

Next, multiply each side of the equation by `color(red)(3)` to eliminate the fraction while keeping the equation balanced:

`color(red)(3)(-x + 2) = color(red)(3) xx (5x - 3)/3`

`(color(red)(3) xx -x) + (color(red)(3) xx 2) = cancel(color(red)(3)) xx (5x - 3)/color(red)(cancel(color(black)(3)))`

`-3x + 6 = 5x - 3`

Then, add `color(red)(3x)` and `color(blue)(3)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`color(red)(3x) - 3x + 6 + color(blue)(3) = color(red)(3x) + 5x - 3 + color(blue)(3)`

`0 + 9 = (color(red)(3) + 5)x - 0`

`9 = 8x`

Now, divide each side of the equation by `color(red)(8)` to solve for `x` while keeping the equation balanced:

`9/color(red)(8) = (8x)/color(red)(8)`

`9/8 = (color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8))`

`9/8 = x`

`x = 9/8`