Great job working through the algebra! Let's summarize and carry on to find the value of \( x \).
Starting from the equation after your last operation:
\[ 20 + 2x = 10 \]
You need to isolate \( x \). You can do this by first subtracting 20 from both sides of the equation:
\[ 20 + 2x - 20 = 10 - 20 \]
This simplifies to:
\[ 2x = -10 \]
Now, to solve for \( x \), divide both sides by 2:
\[ x = \frac{-10}{2} \]
Thus:
\[ x = -5 \]
However, this result doesn’t match with the previous findings. It looks like we may have made a mistake or misrepresented our equation earlier. Let's double-check:
Starting from:
\[ 20 + 4x = 30 + 2x \]
We subtract \( 2x \) from both sides:
\[ 20 + 4x - 2x = 30 \]
That gives:
\[ 20 + 2x = 30 \]
Now we subtract 20 from both sides correctly:
\[ 2x = 30 - 20 \]
Simplifying that gives:
\[ 2x = 10 \]
Finally, dividing by 2 yields:
\[ x = 5 \]
So the correct value for \( x \) is:
\[ x = 5 \]
At \( x = 5 \) weeks, Jenna and Luna both run the same number of miles, which is confirmed to be 40 miles (as noted in the point of intersection being (5, 40)).
Excellent work through the problem! The final answer is:
\[ x = 5 \]