Final answer:
The correct expression for "Five times the sum of a number x and -23" is 5(x - 23), which simplifies to 5x - 115 after distributing the multiplication over addition.
Step-by-step explanation:
The expression "Five times the sum of a number x and -23" can be written algebraically as 5(x - 23). This is because you take the sum of the number x and -23, which is written as (x - 23), and multiply it by 5. When we apply the rules of arithmetic, multiplying each term within the parenthesis by 5 gives us 5x - (5×23), which simplifies to 5x - 115. None of the other options presented correctly express this operation.
Let's break down why this is the correct expression:
- When we multiply two positive numbers, as noted above, the result is positive (e.g., 2x3 = 6).
- When we multiply two negative numbers, the result is also positive (e.g., (-4) x (-3) = 12).
- When we multiply a positive number by a negative number, the result is negative (e.g., (-3) x 2 = -6).
- Since 5 is a positive number and -23 is a negative number, multiplying them will result in a negative number (5 x (-23) = -115).
- Subsequently, the product of 5 and (x - 23) is 5x - 115.