Which verbal expressions can be represented by `2(x-5)`?

Options

A. 5 less than 2 times x
B. 2 multiplied by x less 5
C. Twice the difference of x and 5
D. The product of 2 and x, decreased by 5.

Answer

To determine which verbal expressions can be represented by the expression \(2(x-5)\), we will analyze each option step by step.

### Step 1: Understand the expression
The expression \(2(x-5)\) can be simplified as follows:
\[ 2(x-5) = 2x - 10 \]
This means we are looking for verbal expressions that can be represented by \(2x - 10\).

### Step 2: Analyze each option

**Option 1: "5 less than 2 times x"**
- This can be written mathematically as:
\[ 2x - 5 \]
- Comparing this with \(2(x-5)\) or \(2x - 10\), we see that \(2x - 5\) is not equal to \(2x - 10\).
- **Conclusion:** This option is incorrect.

**Option 2: "2 multiplied by x less 5"**
- This phrase can be interpreted as:
\[ 2x - 5 \]
- Similar to the first option, this is also not equal to \(2x - 10\).
- **Conclusion:** This option is incorrect.

**Option 3: "Twice the difference of x and 5"**
- The difference of \(x\) and \(5\) is \(x - 5\).
- Therefore, twice the difference can be written as:
\[ 2(x - 5) = 2x - 10 \]
- This matches our expression \(2(x-5)\).
- **Conclusion:** This option is correct.

**Option 4: "The product of 2 and x decreased by 5"**
- This can be written mathematically as:
\[ 2x - 5 \]
- Again, this is not equal to \(2x - 10\).
- **Conclusion:** This option is incorrect.

### Final Conclusion
The only verbal expression that can be represented by \(2(x-5)\) is:
- "Twice the difference of x and 5."