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?

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Answer 1

Let's solve this problem step by step.

### Part A: Simplifying the Expression

The expression given is:

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

First, we'll distribute the terms:

1. Distributing \(4\) across \((3x - 1)\):

\[
4(3x) - 4(1) = 12x - 4
\]

2. Distributing \(-2\) across \((6 + 2x)\):

\[
-2(6) - 2(2x) = -12 - 4x
\]

Now, we can combine these results:

\[
12x - 4 - 12 - 4x
\]

Now combine like terms:

1. Combine \(12x\) and \(-4x\):

\[
12x - 4x = 8x
\]

2. Combine \(-4\) and \(-12\):

\[
-4 - 12 = -16
\]

Putting it all together, the simplified expression is:

\[
8x - 16
\]

### Part B: Evaluating the Expression for \(x = 12.5\)

Now, we need to evaluate the simplified expression \(8x - 16\) at \(x = 12.5\):

\[
8(12.5) - 16
\]

Calculating \(8(12.5)\):

\[
8 \times 12.5 = 100
\]

Now substituting this back into the expression:

\[
100 - 16 = 84
\]

### Final Answers:

- **Part A:** The simplified form of the expression is \(8x - 16\).
- **Part B:** The store received \(84\) articles of clothing last Thursday when \(x = 12.5\).