Solve the following inequality and graph the solution set on a number line.
\[
3 x-6> 2 x+9
\]
What is the solution?
$\{x \mid \square$ (Type an inequality.)
Choose the correct graph below.
A.
B.
c.
D.

Answer

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Answer

The correct graph would be a number line with an open circle at 15 and shading to the right.

Steps

Step 1 ：Subtract 2x from both sides of the inequality: $3x - 2x > 2x + 9 - 2x$ which simplifies to $x > 2x + 9$.

Step 2 ：Add 6 to both sides of the inequality: $x + 6 > 2x + 9 + 6$ which simplifies to $x > 15$.

Step 3 ：The solution to the inequality is $\boxed{x > 15}$. This means that any number greater than 15 is a solution to the inequality.

Step 4 ：The correct graph would be a number line with an open circle at 15 and shading to the right.