The correct graph of the solution set of |3x+1| =5 is the graph (b).
Here's how we can analyze the answer choices:
Graph (a): This graph shows a parabola, which is not the correct shape for the absolute value function.
Graph (b): This graph shows two lines, one at x = -2 and the other at x = -4/3. This is correct because the absolute value function |3x + 1| = 5 can be rewritten as two equations: 3x + 1 = 5 and 3x + 1 = -5. Solving these equations gives us x = -2 and x = -4/3, respectively.
Graph (c): This graph shows two vertical lines at x = -2 and x = -4/3, but they extend infinitely in both directions. This is incorrect because the absolute value function only considers non-negative values inside the absolute value bars.
Graph (d): This graph shows a triangle with vertices at (-2, 0), (-4/3, 0), and (-2, 5). This is incorrect because the absolute value function does not have a triangular shape.
Therefore, the graph of the solution set of |3x+1| =5 is the graph (b) that shows two vertical lines at x = -2 and x = -4/3.
The question probable may be:
which is the graph of the solution set of |3x+1| =5