Question

Use this information to answer the following questions.
Three expressions are shown.
Expression 1
StartFraction 324 Over 84 EndFraction
Expression 2
7 left parenthesis 6 x minus 3 right parenthesis
Expression 3
negative three halves left parenthesis 12 x minus 6 right parenthesis
Question content area bottom
Part 1
Which number is equivalent to the sum of expression 2 and expression​ 3?
A.46 x minus 21
46 x minus 21
B.24 x minus 30
24 x minus 30
C.60 x minus 30
60 x minus 30
D.24 x minus 12
24 x minus 12

Answer 1

To find the sum of Expression 2 and Expression 3, let's simplify each expression first and then add them together.

**Expression 2:**
\[
7(6x - 3)
\]
Distributing the 7:
\[
= 7 \cdot 6x - 7 \cdot 3
\]
\[
= 42x - 21
\]

**Expression 3:**
\[
-\frac{3}{2}(12x - 6)
\]
Distributing \(-\frac{3}{2}\):
\[
= -\frac{3}{2} \cdot 12x + \frac{3}{2} \cdot 6
\]
Calculating each part:
\[
= -18x + 9
\]

Now, we add Expression 2 and Expression 3:
\[
(42x - 21) + (-18x + 9)
\]
Combining like terms:
- For \(x\) terms: \(42x - 18x = 24x\)
- For constant terms: \(-21 + 9 = -12\)

Thus, the sum of Expression 2 and Expression 3 is:
\[
24x - 12
\]

Now, looking at the options provided:
A. \(46x - 21\)
B. \(24x - 30\)
C. \(60x - 30\)
D. \(24x - 12\)

The correct choice is **D. \(24x - 12\)**.