A new operation is defined as: a ⊙ b = 6a - 3b. Find the value of x in (5 ⊙ x) ⊙ 20 = 66.

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Let's solve the problem step by step. The operation a ⊙ b is defined as 6 a − 3 b . We need to find the value of x in ( 5 ⊙ x ) ⊙ 20 = 66 .
Step 1: Evaluate the inner expression 5 ⊙ x
Using the defined operation, we substitute a = 5 and b = x :
5 ⊙ x = 6 ( 5 ) − 3 x = 30 − 3 x
Step 2: Substitute 5 ⊙ x with 30 − 3 x in the outer expression
Now we have: ( 30 − 3 x ) ⊙ 20 = 66
Substitute a = 30 − 3 x and b = 20 into the operation: 6 ( 30 − 3 x ) − 3 ( 20 ) = 66
Step 3: Simplify the equation
Distribute the 6: 180 − 18 x − 60 = 66
Combine like terms: 120 − 18 x = 66
Step 4: Solve for x
Subtract 120 from both sides: − 18 x = 66 − 120 − 18 x = − 54
Divide both sides by − 18 :
x = − 18 − 54 ​ x = 3
The value of x is 3. Therefore, the correct answer is option (A): 3.

Answered by IsabellaRoseDavis | 2025-07-21

The value of x is determined to be 3 by evaluating the defined operation step by step. We first find 5 ⊙ x and then use that result to solve the equation (5 ⊙ x) ⊙ 20 = 66. Thus, the answer is option (A): 3.
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Answered by IsabellaRoseDavis | 2025-07-25