Question

How do you solve `(X+3)/(2) -(X-4)/(7) = 1`?

Answer 1

See the entire solution process below.

Explanation:

First, multiply each side of the equation by the lowest common denominator for both fractions, `color(red)(14)`, to eliminate the fractions while keeping the equation balanced:

`color(red)(14)((X + 3)/2 - (X - 4)/7) = color(red)(14) xx 1`

`(color(red)(14) xx (X + 3)/2) - (color(red)(14) xx (X - 4)/7) = 14`

`(cancel(color(red)(14))7 xx ((X + 3))/color(red)(cancel(color(black)(2)))) - (cancel(color(red)(14))2 xx ((X - 4))/color(red)(cancel(color(black)(7)))) = 14`

`7(X + 3) - 2(X - 4) = 14`

`7X + 21 - 2X + 8 = 14`

`5X + 29 = 14`

`5X + 29 - color(red)(29) = 14 - color(red)(29)`

`5X + 0 = -15`

`5X = -15`

`(5X)/color(red)(5) = -15/color(red)(5)`

`(color(red)(cancel(color(black)(5)))X)/cancel(color(red)(5)) = -3`

`X = -3`

Answer 2

`x=-3`

Explanation:

Making the denominators all the same.

`" "color(green)([ (x+3)/2color(red)(xx1)]" " -" "[(x-4)/7color(red)(xx1)]=[1color(red)(xx1)]`

`" "color(green)([ (x+3)/2color(red)(xx7/7)]color(white)(..) -color(white)(.)[(x-4)/7color(red)(xx2/2)]=[1color(red)(xx14/14)]`

`" "color(green)([ (7x+21)/14]" "color(white)(.) -color(white)(...)[(2x-8)/14]" "=" "[14/14]`

Multiply everything by 14

`" "color(green)(7xcolor(red)(+21) -2xcolor(red)(+8)=14)`

`" "color(green)(7x-2xcolor(red)(+21+8)=14 )larr` Regrouped

`" "5x+29=14`

Subtract 29 from both sides

`" "5x=-15`

Divide both sides by 5

`" "x=-3`