Evaluate $3(x-4)+2 x-x^2$ for $x=5$
A. -12
B. 0
C. -4
D. 40
Answer (1)
Substitute x = 5 into the expression 3 ( x − 4 ) + 2 x − x 2 .
Simplify the expression using the order of operations.
Calculate the result: 3 ( 5 − 4 ) + 2 ( 5 ) − ( 5 ) 2 = 3 ( 1 ) + 10 − 25 = 3 + 10 − 25 = − 12 .
The final answer is − 12 .
Explanation
Understanding the Problem We are given the expression 3 ( x − 4 ) + 2 x − x 2 and we need to evaluate it at x = 5 .
Substitution Substitute x = 5 into the expression:
3 ( 5 − 4 ) + 2 ( 5 ) − ( 5 ) 2
Simplification Simplify the expression using the order of operations:
3 ( 1 ) + 10 − 25
3 + 10 − 25
13 − 25
− 12
Final Answer The value of the expression 3 ( x − 4 ) + 2 x − x 2 when x = 5 is − 12 .
Examples
Evaluating algebraic expressions is a fundamental skill in mathematics with numerous real-world applications. For instance, consider a scenario where a company's profit is modeled by the expression P ( x ) = 3 ( x − 4 ) + 2 x − x 2 , where x represents the number of units sold. By evaluating this expression at a specific value of x , such as x = 5 , the company can determine its profit when 5 units are sold. This type of evaluation is crucial for making informed business decisions, forecasting revenue, and optimizing production strategies.
