Simplify (3x – 4)-(5x -3). (1)-2r 7 (2) -2x -1 (3) 2x -1 (4) 2x-7 .
The Correct Answer and Explanation is :
Let’s simplify the expression ((3x – 4) – (5x – 3)).
Step 1: Distribute the negative sign
When you subtract the second expression ((5x – 3)), you need to distribute the negative sign across the terms inside the parentheses. This means:
[
(3x – 4) – (5x – 3) = 3x – 4 – 5x + 3
]
Step 2: Combine like terms
Now, combine the like terms (the terms with (x) and the constant terms):
- Combine the (x)-terms: (3x – 5x = -2x)
- Combine the constant terms: (-4 + 3 = -1)
Thus, the simplified expression is:
[
-2x – 1
]
Step 3: Match with options
Now that we have simplified the expression to (-2x – 1), let’s compare it with the options given:
- (-2r 7)
- (-2x – 1) (this is the correct option)
- (2x – 1)
- (2x – 7)
Correct answer: Option (2) (-2x – 1)
Explanation:
The problem requires simplifying a linear expression involving parentheses. The key to simplifying such expressions is distributing any negative signs and then combining like terms (terms with the same variable and constants). Here, after distributing the negative sign and combining terms, the expression simplifies to (-2x – 1). This type of simplification is a fundamental skill in algebra, and it allows you to express the given mathematical relationship in a simpler, more usable form.
Now, I will generate an image representing the solution process.
Here is the step-by-step visual representation of simplifying the expression ((3x – 4) – (5x – 3)). It clearly shows how to distribute the negative sign, combine like terms, and arrive at the simplified expression (-2x – 1). Let me know if you’d like further explanation or if you have any other questions!
