Final answer:
To graph the solution set of ||5x-3||-6=-2x+12, isolate the absolute value term and split the equation into two cases. Solve each case separately to find the solutions. Plot the solutions on a number line and shade the region between them.
Step-by-step explanation:
To graph the solution set of ||5x-3||-6=-2x+12, we need to solve the equation first. Let's start by isolating the absolute value term. Adding 6 to both sides gives us ||5x-3|| = -2x + 18. Now we can split the equation into two cases: 5x-3 = -2x + 18 and 5x-3 = 2x - 18.
Solving the first case: Adding 2x and 3 to both sides gives us 7x = 21, so x = 3.
Solving the second case: Adding 2x and 3 to both sides gives us 3x = 15, so x = 5.
Therefore, the solution set is {3, 5}. To graph these values, plot the points (3, 0) and (5, 0) on a number line and shade the region between them.