Question

How do you solve `2x-4/7=1/2x+9/14`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(14)` to eliminate the fractions while keeping the equation balanced. It will be easier to solve the equation without fractions and `color(red)(14)` is the lowest common denominator for the three fractions:

`color(red)(14)(2x - 4/7) = color(red)(14)(1/2x + 9/14)`

`(color(red)(14)xx 2x) - (color(red)(14)xx 4/7) = (color(red)(14) xx 1/2x) + (color(red)(14)xx 9/14)`

`28x - (cancel(color(red)(14)) 2 xx 4/color(red)(cancel(color(black)(7)))) = (cancel(color(red)(14)) 7 xx 1/color(red)(cancel(color(black)(2)))x) + (cancel(color(red)(14)) xx 9/color(red)(cancel(color(black)(14))))`

`28x - 8 = 7x + 9`

Next, add `color(red)(8)` and subtract `color(blue)(7x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`28x - 8 + color(red)(8) - color(blue)(7x) = 7x + 9 + color(red)(8) - color(blue)(7x)`

`28x - color(blue)(7x) - 8 + color(red)(8) = 7x - color(blue)(7x) + 9 + color(red)(8)`

`28x - color(blue)(7x) - 8 + color(red)(8) = 7x - color(blue)(7x) + 9 + color(red)(8)`

`21x - 0 = 0 + 17`

`21x = 17`

Now, divide each side of the equation by `color(red)(21)` to solve for `x` while keeping the equation balanced:

`(21x)/color(red)(21) = 17/color(red)(21)`

`(color(red)(cancel(color(black)(21)))x)/cancel(color(red)(21)) = 17/21`

`x = 17/21`