Question

solve the inequality. graph the solution set and write it in interval notation. 3x(x + 3)>3x² - 4x + 39. choose the correct graph below. a. -10 0 3 10 b. 0 3 c. 0 3 d. 0 3 write the answer in interval notation.

Explanation:

Step1: Expand the left - hand side

Expand $3x(x + 3)$ to get $3x^{2}+9x$. The inequality becomes $3x^{2}+9x>3x^{2}-4x + 39$.

Step2: Subtract $3x^{2}$ from both sides

$3x^{2}+9x-3x^{2}>3x^{2}-4x + 39-3x^{2}$, which simplifies to $9x>-4x + 39$.

Step3: Add $4x$ to both sides

$9x + 4x>-4x+4x + 39$, resulting in $13x>39$.

Step4: Divide both sides by 13

$\frac{13x}{13}>\frac{39}{13}$, so $x > 3$.

Answer:

The solution in interval notation is $(3,\infty)$. The correct graph would be a number - line with an open circle at $x = 3$ and an arrow pointing to the right. Without seeing the full details of the graphs A, B, C, D, we can't choose a specific graph among them, but the solution set corresponds to a graph that has an open - circle at 3 and shading to the right.