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

To solve the problem, we'll break it down into two parts: Part A (simplifying the expression) and Part B (finding the value when \( x = 12.5 \)).

### Part A: Simplification

The given expression is:

\[
4(3x - 1) - 2(6 + 2x)
\]

Let's simplify this step by step.

1. Distribute \( 4 \) and \( -2 \):

\[
= 4 \cdot 3x - 4 \cdot 1 - 2 \cdot 6 - 2 \cdot 2x
\]
\[
= 12x - 4 - 12 - 4x
\]

2. Combine like terms:

\[
= 12x - 4x - 4 - 12
\]
\[
= (12x - 4x) + (-4 - 12)
\]
\[
= 8x - 16
\]

So, the simplified form of the expression is:

\[
\boxed{8x - 16}
\]

### Part B: Evaluating the Expression

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

\[
8(12.5) - 16
\]

1. Calculate \( 8(12.5) \):

\[
8 \cdot 12.5 = 100
\]

2. Now subtract \( 16 \):

\[
100 - 16 = 84
\]

Thus, the number of articles of clothing the store received last Thursday is:

\[
\boxed{84}
\]