Question

1. simplify the expression $3(x - 4) - 2(2x + 1)$.

a. $-x + 7$

b. $-x + 11$

c. $-x - 14$

d. $-x - 7$

Explanation:

Step1: Distribute the coefficients

First, we distribute the 3 in \(3(x - 4)\) and the -2 in \(-2(2x + 1)\). Using the distributive property \(a(b + c)=ab+ac\), we get:
\(3(x - 4)=3x-12\) and \(-2(2x + 1)=-4x - 2\).
So the expression becomes \(3x-12-4x - 2\).

Step2: Combine like terms

Now, we combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(3x-4x=-x\). For the constant terms: \(-12-2=-14\).
Putting these together, we have \(-x-14\).

Answer:

c. \(-x - 14\)