Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far:

. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides.

. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process.

. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.
Answer:
x<25
Step-by-step explanation:
Let's solve your inequality step-by-step.
2.4x−9<1.8x+6
Step 1: Subtract 1.8x from both sides.
2.4x−9−1.8x<1.8x+6−1.8x
0.6x−9<6
Step 2: Add 9 to both sides.
0.6x−9+9<6+9
0.6x<15
Step 3: Divide both sides by 0.6
0.6x/0.6 < 15/0.6
x<25