Question

 

Constructed Response Question

A clothing donation store received numerous articles of clothing on Thursday of last week.  The number of articles of clothing that the store received last Thursday is represented by the expression shown:

4(3x-1)-2(6+2x)

Part A:
What is the simplified form of the expression above?

Part B:
If x=12.5, how many articles of clothing did the store receive last Thursday?

​

Answer 1

Part A:

To simplify the expression \( 4(3x - 1) - 2(6 + 2x) \), we start by distributing the constants outside the parentheses.

1. Distribute \( 4 \) in \( 4(3x - 1) \):
\[
4 \cdot 3x - 4 \cdot 1 = 12x - 4
\]

2. Distribute \( -2 \) in \( -2(6 + 2x) \):
\[
-2 \cdot 6 - 2 \cdot 2x = -12 - 4x
\]

Next, we combine the results:
\[
12x - 4 - 12 - 4x
\]

Now, combine like terms. Start with the \( x \) terms:
\[
12x - 4x = 8x
\]

Then, combine the constant terms:
\[
-4 - 12 = -16
\]

Putting it all together, the simplified expression is:
\[
\boxed{8x - 16}
\]

---

Part B:

Next, we substitute \( x = 12.5 \) into the simplified expression \( 8x - 16 \):

1. Substitute \( x \):
\[
8(12.5) - 16
\]

2. Calculate \( 8(12.5) \):
\[
8 \cdot 12.5 = 100
\]

3. Now subtract \( 16 \):
\[
100 - 16 = 84
\]

Therefore, the number of articles of clothing the store received last Thursday is:
\[
\boxed{84}
\]