Three times a number `x` is equal to `12` less than twice the number `y`. Express this statement using literal numbers, numbers and the signs of basic operations.

Options

A. `x=2y+12`
B. `3x=2y+12`
C. `3x=y+12`
D. `3x=y-12`

Answer

To express the statement "Three times a number `x` is equal to `12` less than twice the number `y`" using literal numbers, numbers, and the signs of basic operations, we can follow these steps:

### Step-by-Step Solution:

1. **Identify "Three times a number `x`":**
- This phrase means we need to multiply `x` by `3`.
- Therefore, we can express this as:
\[ 3x \]

2. **Identify "Twice the number `y`":**
- "Twice" means to multiply by `2`, so we multiply `y` by `2`.
- This can be expressed as:
\[ 2y \]

3. **Identify "12 less than twice the number `y`":**
- The phrase "12 less than" indicates that we need to subtract `12` from `2y`.
- This can be expressed as:
\[ 2y - 12 \]

4. **Combine the expressions:**
- The statement says that "Three times a number `x` is equal to `12` less than twice the number `y`".
- This means we set the two expressions equal to each other:
\[ 3x = 2y - 12 \]

### Final Expression:
The final expression of the statement using literal numbers, numbers, and signs of basic operations is:
\[ 3x = 2y - 12 \]