answer:
To graph the equation 3 + 2 | 2/3m - 6| = 27, we can follow these steps:
1. Begin by isolating the absolute value term. To do this, subtract 3 from both sides of the equation:
2 |2/3m - 6| = 24
2. Divide both sides of the equation by 2 to simplify:
|2/3m - 6| = 12
3. Now, we can split the equation into two separate cases, one for when the absolute value expression is positive and one for when it is negative:
Case 1: 2/3m - 6 is positive:
In this case, we can rewrite the equation as:
2/3m - 6 = 12
Case 2: 2/3m - 6 is negative:
In this case, we need to negate the absolute value expression:
-(2/3m - 6) = 12
4. Solve each case separately:
Case 1:
Add 6 to both sides of the equation:
2/3m = 18
Multiply both sides of the equation by 3/2 to isolate m:
m = 27
Case 2:
Distribute the negative sign:
-2/3m + 6 = 12
Subtract 6 from both sides of the equation:
-2/3m = 6
Multiply both sides of the equation by -3/2 to isolate m:
m = -9
5. Plot the points (27, 0) and (-9, 0) on the x-axis, as these are the solutions we found for m.
6. Draw a line passing through these two points. This line represents the graph of the equation 3 + 2 | 2/3m - 6| = 27.
In summary, the graph of the equation 3 + 2 | 2/3m - 6| = 27 is a straight line passing through the points (27, 0) and (-9, 0).