Question

1. which expression is equivalent to the expression shown below?

6(2x - 1) - 4x + 9
a. 8x - 15
b. 8x + 8
c. 16x + 3
d. 8x + 3

Explanation:

Step1: Distribute the 6

Using the distributive property \( a(b + c)=ab+ac \), we distribute 6 to \( 2x \) and \( -1 \):
\( 6(2x - 1)=6\times2x-6\times1 = 12x-6 \)
So the expression becomes \( 12x - 6-4x + 9 \)

Step2: Combine like terms (x - terms)

Combine \( 12x \) and \( - 4x \):
\( 12x-4x=8x \)
Now the expression is \( 8x-6 + 9 \)

Step3: Combine like terms (constant terms)

Combine \( -6 \) and \( 9 \):
\( -6 + 9=3 \)
So the simplified expression is \( 8x + 3 \)

Answer:

D. \( 8x + 3 \)