What is $-3x + 1$ subtracted from $3x - 1$?
A. $6x - 2$
B. -2
C. 6x
D. $-6x + 2$
Answer (2)
Subtract − 3 x + 1 from 3 x − 1 : ( 3 x − 1 ) − ( − 3 x + 1 ) .
Distribute the negative sign: 3 x − 1 + 3 x − 1 .
Combine like terms: 6 x − 2 .
The result of the subtraction is 6 x − 2 .
Explanation
Understanding the Problem We are asked to subtract − 3 x + 1 from 3 x − 1 . This means we need to perform the operation ( 3 x − 1 ) − ( − 3 x + 1 ) .
Distributing the Negative Sign To subtract the expression, we distribute the negative sign to both terms inside the parentheses: 3 x − 1 − ( − 3 x ) − ( 1 ) = 3 x − 1 + 3 x − 1 .
Combining Like Terms Now, we combine the like terms. We have two terms with x , which are 3 x and 3 x , and two constant terms, which are − 1 and − 1 . Combining these, we get ( 3 x + 3 x ) + ( − 1 − 1 ) .
Simplifying the Expression Simplifying the expression, we have 6 x − 2 .
Final Answer Therefore, − 3 x + 1 subtracted from 3 x − 1 is 6 x − 2 .
Examples
In real life, this kind of subtraction of expressions can be used in budgeting. Imagine you have a certain income ( 3 x − 1 ) and certain expenses ( − 3 x + 1 ). Subtracting the expenses from the income gives you the remaining balance ( 6 x − 2 ). Understanding how to manipulate these expressions helps you manage your finances effectively.
The expression − 3 x + 1 subtracted from 3 x − 1 simplifies to 6 x − 2 . Therefore, the correct answer is option A, 6 x − 2 .
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