If a*b = a+3b-5 and a `aob=2a-b, AA a,b in z` then `(2*3) 0 5=`

Options

A. 2
B. 3
C. `-7`
D. 7

Answer

To solve the problem, we need to evaluate the expression \( (2 * 3) \odot 5 \) using the definitions of the operations \( * \) and \( \odot \).

### Step 1: Calculate \( 2 * 3 \)
According to the problem, the operation \( a * b \) is defined as:
\[ a * b = a + 3b - 5 \]
Substituting \( a = 2 \) and \( b = 3 \):
\[ 2 * 3 = 2 + 3(3) - 5 \]
Calculating this step-by-step:
- First, calculate \( 3(3) = 9 \)
- Then, substitute back: \( 2 + 9 - 5 \)
- Now calculate \( 2 + 9 = 11 \)
- Finally, \( 11 - 5 = 6 \)

So, we find:
\[ 2 * 3 = 6 \]

### Step 2: Calculate \( 6 \odot 5 \)
Now we need to use the result from Step 1 in the operation \( \odot \). The operation \( a \odot b \) is defined as:
\[ a \odot b = 2a - b \]
Substituting \( a = 6 \) and \( b = 5 \):
\[ 6 \odot 5 = 2(6) - 5 \]
Calculating this step-by-step:
- First, calculate \( 2(6) = 12 \)
- Then, substitute back: \( 12 - 5 \)
- Finally, \( 12 - 5 = 7 \)

So, we find:
\[ 6 \odot 5 = 7 \]

### Final Result
Thus, the value of \( (2 * 3) \odot 5 \) is:
\[ \boxed{7} \]