Question

3(x - 4) + 8(2x + 4)
choose the correct answer
a. 24(3x)
b. 19x + 20
c. 14x - 20

Explanation:

Step1: Distribute the coefficients

First, we distribute the 3 into \((x - 4)\) and the 8 into \((2x + 4)\).
For \(3(x - 4)\), using the distributive property \(a(b + c)=ab+ac\) (here \(a = 3\), \(b=x\), \(c=-4\)), we get \(3\times x-3\times4 = 3x-12\).
For \(8(2x + 4)\), using the distributive property, we get \(8\times2x+8\times4=16x + 32\).
So the expression becomes \(3x-12 + 16x+32\).

Step2: Combine like terms

Now we combine the \(x\)-terms and the constant terms.
The \(x\)-terms are \(3x\) and \(16x\). Combining them: \(3x+16x=(3 + 16)x=19x\).
The constant terms are \(- 12\) and \(32\). Combining them: \(-12 + 32=20\).
Putting it together, we get \(19x+20\).

Answer:

B. \(19x + 20\)