Answer: x = 6
Step-by-step explanation: Before we solve for x, we can note that the triangles are similar by the Angle-Angle Postulate. Given the triangles are similar, we can set up a proportion:
[tex]\dfrac{x}{4} = \dfrac{x + 3}{6}[/tex]
Next, we cross-multiply:
[tex]6x = 4x + 12[/tex]
Then, we subtract 4x from both sides:
[tex]2x = 12[/tex]
Finally, we divide by the coefficient (2):
[tex]\dfrac{2x}{2} = x\\\\\dfrac{12}{2} = 6[/tex]
Therefore, x = 6.
