Final answer:
To find the sum or difference, expand the expression 9(x-4) to get 9x-36, and combine with the second expression (2x-14) to get the sum as 11x-50 and the difference as 7x-22 by combining like terms.
Step-by-step explanation:
To find the sum or difference of 9(x-4) and (2x-14), we need to expand and then combine like terms. First, we distribute the 9 to both x and -4 in the first expression, getting 9x - 36. The second expression is already simplified, so we keep it as 2x - 14. Next, we combine like terms by adding (or subtracting) the coefficients of the x terms and the constant terms separately:
- Sum: (9x + 2x) + (-36 - 14) = 11x - 50
- Difference: (9x - 2x) - (-36 + 14) = 7x - 22
The sum of the expressions is 11x - 50 and the difference is 7x - 22. This process involves combining like terms and simplifying expressions, which are fundamental concepts in algebra.