The length of the radius of the dartboard is 9 in. The diameter is represented by the expression 3xplus6. Write an equation that you can use to solve for x. Then solve for x.

Question

Question content area bottom
Part 1
Write an equation that you can use to solve for x. Choose the correct answer below.
A.3 x plus 6 equals 11
3 x plus 6 equals 11
B.3 x plus 6 equals 9
3 x plus 6 equals 9
C.3 x plus 6 equals 7
3 x plus 6 equals 7
D.3 x plus 6 equals 18
3 x plus 6 equals 18

Answer 1

To find the diameter of the dartboard using the given radius, you can use the relationship between the radius and diameter. The diameter \(d\) is twice the length of the radius \(r\):

\[ d = 2r \]

Given that the radius of the dartboard is 9 inches, we find the diameter:

\[ d = 2 \times 9 = 18 \text{ inches} \]

The diameter is also represented by the expression \(3x + 6\). Therefore, we set up the following equation:

\[ 3x + 6 = 18 \]

Thus, the correct answer is:

D. \(3x + 6 = 18\)

Now, let's solve the equation for \(x\):

1. Subtract 6 from both sides:

   \[ 3x + 6 - 6 = 18 - 6 \]

   \[ 3x = 12 \]

2. Divide both sides by 3:

   \[ x = \frac{12}{3} \]

   \[ x = 4 \]

So, the solution for \(x\) is:

\(x = 4\).