-2I3mI+3<-51
negative two times absolute value 3m is less than negative fifty one
subtracting 3 ... -2 I3mI < -54
dividing by -2 ... I3mI > 27 ... arrowhead changes direction
3m > 27 ... m > 9
-3m > 27 ... m < -9
-2(3m) + 3 < 51
-6m < 51 - 3
Divide both sides by -6, but don't forget to reverse the carat.
-2I3mI+3<-51
| 3m | > 27
± 3m > 27
3m > 27 OR -3m > 27
m > 9 OR m < -9 , confirming R_scott.
To solve the inequality -2|3m| + 3 < -51, we need to isolate the variable "m" on one side of the inequality sign. Here's how:
Step 1: Start by isolating the absolute value term. Since -2|3m| is negative, we can remove the absolute value bars by multiplying both sides of the inequality by -1. However, when we multiply by a negative number, we need to reverse the direction of the inequality sign. The inequality becomes:
2|3m| - 3 > 51
Step 2: Next, remove the constant term by subtracting 3 from both sides of the inequality:
2|3m| > 54
Step 3: Divide both sides of the inequality by 2 to isolate the absolute value term:
|3m| > 27
Step 4: Now, we need to consider two cases: 3m is either positive or negative.
Case 1: If 3m is positive, we can simply remove the absolute value bars and keep the inequality sign:
3m > 27
Divide both sides of the inequality by 3:
m > 9
Case 2: If 3m is negative, we have to remove the absolute value bars and reverse the inequality sign:
-3m > 27
Divide both sides of the inequality by -3:
m < -9
So, the solutions for the inequality -2|3m| + 3 < -51 are m > 9 (for positive values of 3m) and m < -9 (for negative values of 3m).