To find the value of \( x \), we can set up an equation based on the relationship between the distances. The total distance from Anoa to Jamie can be expressed as:
\[ \text{Distance from Anoa to Madison} + \text{Distance from Madison to Jamie} = \text{Distance from Anoa to Jamie} \]
Substituting the given distances:
\[ (3x + 2) + (3x + 4) = 9x - 3 \]
Combining the distances on the left side:
\[ 3x + 2 + 3x + 4 = 9x - 3 \] \[ 6x + 6 = 9x - 3 \]
Next, we solve for \( x \) by isolating \( x \):
- Subtract \( 6x \) from both sides:
\[ 6 = 3x - 3 \]
- Next, add \( 3 \) to both sides:
\[ 9 = 3x \]
- Divide both sides by \( 3 \):
\[ x = 3 \]
Now that we have found \( x \), we can find the distance between Madison's house and Jamie's house. The distance is represented by:
\[ 3x + 4 \]
Substituting \( x = 3 \):
\[ 3(3) + 4 = 9 + 4 = 13 \]
Therefore, the value of \( x \) is \( 3 \) and the distance between Madison's house and Jamie's house is \( 13 \) miles.
In summary, \[ x = 3 \quad \text{and the distance between Madison's house and Jamie's house is } 13 \text{ miles.} \]
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