How do you solve #|8x + 1| >23#?
With absolute value inequalities, I find the most useful technique is to solve the inequality twice, once when the expression in the absolute value is positive and once when it is negative and combining those two results.
To find out where the absolute value goes from positive to negative we need to solve for when
This means we need to look at when
In this case, we can just remove the absolute value since the expression is positive anyway:
In this case the absolute value would flip the sign, so we need to add a negative sign in front to remove it:
Now we want to divide by
Now that we know that the inequality holds when