Final answer:
To find AB, set up an equation by equating AL to half of AB. Solve for x and substitute the value back into AL or AB to find the length.
Step-by-step explanation:
To find AB, we need to equate AL to AB using the fact that L is the midpoint of AB. We have AL = 3x + 4 and AB = 10x - 10. Since L is the midpoint, AL must be equal to half of AB. Setting up the equation, we get: 3x + 4 = (10x - 10) / 2. To solve for x, we can cross multiply and simplify: 6x + 8 = 10x - 10. Rearranging the terms, we get: 4x = 18. Dividing both sides by 4, we find: x = 4.5. Finally, substituting the value of x back into either AL or AB, we can find the length of AB. Plugging in x = 4.5 into AL = 3x + 4, we get: AL = 3(4.5) + 4 = 13.5 + 4 = 17.5. Since L is the midpoint, AB = 2AL, so AB = 2(17.5) = 35.