Question

How do you solve the equation `abs(5-6x)=7`?

Answer 1

`x=-1/3" or "x=2`

Explanation:

`"the expression inside the absolute value can be positive or"`
`"negative"`

`rArr5-6x=color(red)(+-)7`

`color(blue)"first solution"`

`5-6x=color(red)(+)7`

`"subtract 5 from both sides"`

`rArr-6x=2`

`"divide both sides by - 6"`

`rArrx=2/(-6)=-1/3`

`color(blue)"second solution"`

`5-6x=color(red)(-)7`

`"subtract 5 from both sides"`

`rArr-6x=-12`

`"divide both sides by - 6"`

`rArrx=(-12)/(-6)=2`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`x=-1/3to|5+2|=|7|=7`

`x=2to|5-12|=|-7|=7`

`rArrx=-1/3" or "x=2" are the solutions"`