Question

Which expression is equivalent to the given expression?

3(x - 7) + 4(12 – 21 + 9)

A) 3x - 21 + 4(12 – 21 + 9)
B) 3x - 21 + 4(12 – 30 + 9)
C) 3x - 21 + 4(0)
D) 3x - 21 + 4(12 – 21 – 9)

Answer 1

The equivalent expression to 3(x - 7) + 4(12 – 21 + 9) is 3x - 21 + 4(0), as option C states, after simplifying the expression inside the parentheses to zero and applying the distributive property.

Step-by-step explanation:

To find an expression equivalent to 3(x - 7) + 4(12 – 21 + 9), we need to simplify the expressions inside the parentheses and then apply the distributive property. First, simplify the expression inside the second set of parentheses: 12 – 21 + 9 equals 0. This simplification leads us to option C because:

• 3(x – 7) simplifies to 3x - 21 (applying the distributive property).
• 4(12 – 21 + 9) simplifies to 4(0) or just 0 when multiplied (since any number multiplied by zero equals zero).
• Adding the two parts together gives 3x - 21.

Therefore, the equivalent expression is 3x - 21 + 4(0), which corresponds to option C.