Question

How do you solve `3|3q-2|=21`?

Answer 1

`q=3" or " q=-5/3`

Explanation:

Isolate the `color(blue)"absolute value"` by dividing both sides of the equation by 3

`cancel(3)^1/cancel(3)^1|3q-2|=21/3`

`rArr|3q-2|=7`

There are 2 solutions to the equation.

`"Solve "3q-2=color(red)(+-)7`

`color(blue)"Solution 1"`

`3q-2=color(red)(+7)rArr3q=7+2=9rArrq=9/3=3`

`color(blue)"Solution 2"`

`3q-2=color(red)(-7)rArr3q=-7+2=-5rArrq=-5/3`

`color(blue)"As a check"`

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

`• x=3to3|9-2|=3xx7=21`

`• x=-5/3to3|-5-2|=3xx|-7|=3xx7=21`

`rArrx=3" or " x=-5/3" are the solutions"`