Final answer:
To solve for x, we set the algebraic expressions for the trisected segments equal to each other and solve the resulting equation. By setting (5x - 7) equal to (2x - 6), we find that x equals 1/3.
Step-by-step explanation:
The student's question involves trisecting a line segment, which means dividing the segment into three equal parts. To solve for x, each segment's algebraic expression should be set equal since they are all equal in length when a segment is trisected. Given the expressions (5x - 7), (2x - 6), (3x - 5), and (4x - 8), we know that the segments represented by these expressions are equal to each other. Therefore, we can set any two of them equal to find the value of x.
For instance, if we set (5x - 7) equal to (2x - 6), we can solve for x:
- 5x - 7 = 2x - 6
- 3x = 1 (by adding 7 to both sides and subtracting 2x from both sides)
- x = 1/3 (dividing both sides by 3)
This value can then be substituted back into each expression to verify that they indeed represent equal segments.