Final answer:
The algebraic problem is solved by setting x as the number of books Zach read and creating an equation based on the given relationship between the number of books Paige and Zach read. The total number of books read combined is 25, with Paige reading 7 more than Zach. Solving the equation, Zach read 9 books.
Step-by-step explanation:
The student's question revolves around an algebraic problem where Paige and Zach read a total of 25 books over the summer and Paige read 7 more books than Zach. We are to express the number of books Zach read using a variable x.
To frame the equation, we let the number of books Zach read be x. According to the problem, Paige read 7 more books than Zach, so Paige read x + 7 books. Together, they read a total of 25 books, so we can write the equation as x (books Zach read) + x + 7 (books Paige read) = 25 (total books read). Combining like terms, we get 2x + 7 = 25. To find the value of x, we solve for x by first subtracting 7 from both sides of the equation, yielding 2x = 18. Dividing both sides by 2 gives us x = 9. Therefore, Zach read 9 books over the summer.