Evaluate the expression $2 x-(4 y-3)+5 x z$, when $x=-3, y=2$, and $z=-1$.
A. 45
B. 16
C. 4
D. -10
Answer (2)
Substitute the given values: x = − 3 , y = 2 , and z = − 1 into the expression 2 x − ( 4 y − 3 ) + 5 x z .
Simplify the expression: 2 ( − 3 ) − ( 4 ( 2 ) − 3 ) + 5 ( − 3 ) ( − 1 ) = − 6 − ( 8 − 3 ) + 15 = − 6 − 5 + 15 .
Perform the arithmetic operations: − 6 − 5 + 15 = − 11 + 15 = 4 .
The final result is: 4 .
Explanation
Understanding the Problem We are asked to evaluate the expression 2 x − ( 4 y − 3 ) + 5 x z when x = − 3 , y = 2 , and z = − 1 . This involves substituting the given values into the expression and simplifying.
Substitution First, substitute the given values of x , y , and z into the expression: 2 ( − 3 ) − ( 4 ( 2 ) − 3 ) + 5 ( − 3 ) ( − 1 )
Simplification Next, simplify the expression using the order of operations (PEMDAS/BODMAS): 2 ( − 3 ) − ( 8 − 3 ) + 5 ( − 3 ) ( − 1 ) − 6 − ( 5 ) + 5 ( 3 ) − 6 − 5 + 15 − 11 + 15 4
Final Answer Therefore, the value of the expression 2 x − ( 4 y − 3 ) + 5 x z when x = − 3 , y = 2 , and z = − 1 is 4.
Examples
Evaluating algebraic expressions is a fundamental skill in mathematics and has numerous real-world applications. For instance, consider a scenario where a business calculates its profit based on revenue, cost, and other factors. If the revenue is represented by 2 x , the cost by ( 4 y − 3 ) , and other income by 5 x z , then the expression 2 x − ( 4 y − 3 ) + 5 x z represents the total profit. By substituting the values of x , y , and z , the business can quickly determine its profit. This type of calculation is essential for financial planning and decision-making.
The value of the expression 2 x − ( 4 y − 3 ) + 5 x z when substituting x = − 3 , y = 2 , and z = − 1 is 4 .
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