Subtract $(7 x-2)-(3 x-5)$
A. $4 x+7$
B. $4 x-7$
C. $4 x+3$
D. $4 x-3$
Answer (1)
Distribute the negative sign: ( 7 x − 2 ) − ( 3 x − 5 ) = 7 x − 2 − 3 x + 5 .
Combine like terms: 7 x − 3 x − 2 + 5 .
Simplify the expression: 4 x + 3 .
The correct answer is 4 x + 3 .
Explanation
Understanding the Problem We are asked to subtract the expression ( 7 x − 2 ) − ( 3 x − 5 ) . This involves distributing the negative sign and combining like terms to simplify the expression.
Distributing the Negative Sign First, distribute the negative sign in the second term: ( 7 x − 2 ) − ( 3 x − 5 ) = 7 x − 2 − 3 x + 5
Combining Like Terms Next, combine the like terms (terms with 'x' and constant terms): 7 x − 3 x − 2 + 5
Simplifying the Expression Now, simplify the expression by performing the subtraction and addition: 4 x + 3
Choosing the Correct Answer The simplified expression is 4 x + 3 . Comparing this with the given options, we see that it matches option C.
Examples
Understanding how to subtract algebraic expressions is useful in many real-world scenarios. For example, if you are managing a budget and need to calculate the remaining amount after expenses, you might subtract one expression (expenses) from another (income). Suppose your income is represented by 7 x − 2 and your expenses by 3 x − 5 , where x is a variable representing the number of hours worked. Subtracting the expressions gives you the remaining money after expenses, which is 4 x + 3 . This helps in financial planning and resource allocation.
