The solution of the equation |2x+1| = 6x - 15 is x = 4.
How to solve the system of equatios?
Here we want to solve:
|2x+1| = 6x - 15
To do so, we can graph the two equations:
y = |2x + 1|
y = 6x - 15
In the same coordinate axis.
The solutions of the equation |2x+1| = 6x - 15 are the points where the two graphs intercept.
In the image below you can see the graph of the system. There we can see that the graphs intercept at (4, 9), so the solution is x = 4.