Question

How do you solve `|\frac { 2x - 5} { 7} | = 3`?

Answer 1

`color(blue)(barul(|color(white)(4/3)x=13,-8color(white)(3/7)|`

Explanation:

`color(blue)(|(2x-5)/7|=3`

This is an absolute value value equation

So,we can divide the equation into two

`color(green)((2x-5)/7=3` `and` `color(purple)((2x-5)/7=-3`

Solve for both the equations

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(green)(rarr(2x-5)/7=3`

`color(green)(rarr(2x-5)=3*7`

`color(green)(rarr2x-5=21`

`color(green)(rarr2x=21+5`

`color(green)(rarr2x=26`

`color(green)(rarrx=26/2`

`rArrcolor(green)(barul(|color(white)(3/3)x=13color(white)(5/6)|`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(purple)(rarr(2x-5)/7=-3`

`color(purple)(rarr(2x-5)=-3*7`

`color(purple)(rarr2x-5=-21`

`color(purple)(rarr2x-5=-21`

`color(purple)(rarr2x=-21+5`

`color(purple)(rarr2x=-16`

`color(purple)(rarrx=-16/2`

`rArrcolor(purple)(barul(|color(white)(3/3)x=-8color(white)(3/3)|`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`:.color(blue)(barul(|color(white)(4/3)x=13,-8color(white)(3/7)|`