Final answer:
The length of segment SQ is found by adding the lengths of segments SG and QG, resulting in the expression 14x - 20.
Step-by-step explanation:
To find the length of segment SQ, we first need to establish the relationship between the segments SG and QG. The length of segment SG is represented by the expression 4x+2, and the length of segment QG is represented by the expression 10x-22. Since SG and QG are parts of the same straight line segment SQ, their lengths can be added together to find the length of SQ.
Therefore, the length of segment SQ equals the sum of the lengths of segments SG and QG:
- SG = 4x + 2
- QG = 10x - 22
- SQ = SG + QG = (4x + 2) + (10x - 22) = 14x - 20
The final expression for the length of segment SQ is 14x - 20.