Answer:
x=5
Explanation:
Let's say the left side has points A, B, and C, with B in the middle, and the right side has points A, E, and D, with E in the middle
The Triangle Proportionality Theorem Converse states that if a line splits two sides of a triangle proportionally, the line is parallel to the remaining line.
Here, we can see that the sides are split into congruent lengths to each other, making their proportions 1:1. This proves the theorem converse, so 5x is parallel to 8x+10. Because the other two sides are connected to each other, with AB being a part of AC and AE being a part of AD, AB is parallel to AC and AE is parallel to AD. Given this, we can say that triangle ABE is similar to triangle ACD.
In a similar triangle, the lines corresponding to each other have the same ratio as other lines. This means that
AB/AC = AE/ED = BE/CD.
We are trying to find BE and CD to solve for x, and we can do this by finding the ratio between them
AC = AB + BC
BC = AB
AC = 2 * AB
AB / (2*AB) = BE / CD
1/2 = 5x/(8x+10)
multiply both sides by 2 to remove a denominator
1 = 10x / (8x+10)
multiply both sides by 8x+10 to remove the other denominator
8x+10 = 10x
subtract 8x from both sides to put the variable and its coefficients on one side
2x = 10
divide both sides by 2 to solve for x
x = 5