Question

which of the following is equivalent to $3(a - 2) - (2a + 4)$?
a. $a - 10$
b. $a + 10$
c. $a + 2$
d. $a \cdot 10$

Explanation:

Step1: Expand the terms

First, we expand \(3(a - 2)\) using the distributive property \(c(a + b)=ca+cb\). So, \(3(a - 2)=3\times a-3\times2 = 3a-6\). Then, we have to subtract \((2a + 4)\), which is the same as adding \(-(2a + 4)\). So the expression becomes \(3a-6-(2a + 4)=3a-6 - 2a-4\).

Step2: Combine like terms

Now, combine the \(a\) terms and the constant terms. For the \(a\) terms: \(3a-2a=a\). For the constant terms: \(-6 - 4=-10\). So putting it together, we get \(a-10\).

Answer:

a. \(a - 10\)