x and y are integers such that $$3 < x < 8$$ $$4 < y < 10$$ and $$x + y = 14$$ Find all the possible values of x. - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 3

Now substituting possible values for y into the equation:

• If $y = 5$, then $x + 5 = 14$ gives $x = 9$ (not valid since x must be less than 8).
• If $y = 6$, then $x + 6 = 14$ gives $x = 8$ (not valid since x must be less than 8).
• If $y = 7$, then $x + 7 = 14$ gives $x = 7$ (valid).
• If $y = 8$, then $x + 8 = 14$ gives $x = 6$ (valid).
• If $y = 9$, then $x + 9 = 14$ gives $x = 5$ (valid).

Thus, the possible values of x are 5, 6, and 7.