When [tex]x =2[/tex], what is [tex]10+3(12 \div(3 x ))=[/tex] ?
A. 12
B. 16
C. 26
D. 34
E. 104
Answer (2)
Substitute x = 2 into the expression.
Simplify inside the parenthesis: 3 t im es 2 = 6 .
Perform the division and multiplication: 12 d i v 6 = 2 , then 3 t im es 2 = 6 .
Add the remaining terms: 10 + 6 = 16 . The final answer is 16 .
Explanation
Understanding the Problem We are given the expression 10 + 3 ( 12 d i v ( 3 x )) and we need to evaluate it when x = 2 .
Substituting the Value of x First, substitute x = 2 into the expression:
10 + 3 ( 12 d i v ( 3 t im es 2 ))
Simplifying the Expression Next, simplify the expression inside the parentheses. We have 3 t im es 2 = 6 , so the expression becomes:
10 + 3 ( 12 d i v 6 )
Now, perform the division: 12 d i v 6 = 2 . The expression is now:
10 + 3 ( 2 )
Then, multiply: 3 t im es 2 = 6 . The expression becomes:
10 + 6
Calculating the Final Result Finally, add: 10 + 6 = 16 . Therefore, when x = 2 , the expression 10 + 3 ( 12 d i v ( 3 x )) evaluates to 16.
Examples
Imagine you are calculating the total cost of an item with a base price and some additional charges. This problem is similar to calculating the final price after applying a discount and adding tax. For example, if an item costs $10 and there is a service fee that involves dividing a fixed amount (12) by a quantity related to the number of items purchased (3x), then multiplying the result by a constant (3), this problem helps you find the final cost. Understanding order of operations is crucial in many real-life financial calculations.
When substituting x = 2 into the expression 10 + 3 ( 12 ÷ ( 3 x )) , it simplifies down to 16 . The answer is B. 16 . This is found by following the order of operations step-by-step.
;
