We are asked to find and graph the solution set for all possible values of j in the given inequality.
|3j-1|+6>0
To do this, let's isolate the absolute value expression first.
Recalling that all absolute value expressions are greater than or equal to zero. It follows then that any absolute value expression is greater than all negative numbers.
|3j-1|≥ 0 ⇒ |3j-1|>-6
This means any value of j will satisfy the inequality. Therefore, there are infinitely many solutions, and the solution set is the set of all real numbers.
We can represent this graphically on a number line by showing that all values are included in the solution set, so all values are shaded.
