Final answer:
To find the value of g given that line segments DE and PL are congruent, we set DE = -11 - 4g equal to PL = 3g + 10 and solve the resulting equation, which gives us g = -3.
Step-by-step explanation:
The value of g is determined by setting the two expressions for congruent line segments DE and PL equal to each other, which gives us the equation -11 - 4g = 3g + 10. To solve for g, we combine like terms and get the equation on one side resulting in -4g - 3g = 10 + 11. Simplifying further, we get -7g = 21. Dividing both sides by -7 to solve for g gives us g = -3.