How is 9|r-2| < -73 no solutions
9(r-2)<-73 or 9(-r+2)<-73
first one:
9 r -18 < -73
9 r < -55
r < -55/9 sure looks like a solution
second one:
-9 r + 18 <-73
9 r -18 > 73
9 r > 91
r >91/9 so second solution
I thought you dont distribute with absolute value
My teacher told me the answer was no solution but I dont know how she got it
To determine if the inequality 9|r-2| < -73 has no solutions, we need to understand the absolute value function and how it behaves.
The absolute value of a number, denoted by |x|, represents the distance between x and zero on the number line. It is always a non-negative value.
For the inequality 9|r-2| < -73 to have solutions, the absolute value term on the left-hand side must be non-negative. However, the right-hand side of the inequality is a negative number (-73).
Since the absolute value of a number cannot be negative, it is not possible for the left-hand side of the inequality to be less than a negative value. Therefore, the inequality 9|r-2| < -73 has no solutions.