Difficulty: Easy
Correct Answer: 4
Explanation:
Introduction:
This problem is a straightforward example of solving a linear equation in one variable. Such equations are a foundation for algebra and appear frequently in aptitude and entrance examinations. The goal is to isolate x on one side of the equation using basic algebraic operations.
Given Data / Assumptions:
Concept / Approach:
To solve a linear equation, we typically collect all x terms on one side and all constant terms on the other side. Then we combine like terms and divide to isolate x. The operations used must be valid on both sides of the equation to maintain equality. Because this is a first degree equation, we expect exactly one solution.
Step-by-Step Solution:
Start with: 5x − 17 = −x + 7 Step 1: Move all x terms to the left side by adding x to both sides. 5x − 17 + x = −x + 7 + x This gives: 6x − 17 = 7 Step 2: Move the constant term −17 to the right side by adding 17 to both sides. 6x − 17 + 17 = 7 + 17 This gives: 6x = 24 Step 3: Divide both sides by 6 to isolate x. x = 24 / 6 = 4 Therefore, x = 4 is the solution.
Verification / Alternative check:
Substitute x = 4 back into the original equation. Left side: 5(4) − 17 = 20 − 17 = 3. Right side: −4 + 7 = 3. Both sides equal 3, so x = 4 satisfies the equation exactly. No other value will do so for a linear equation of this type.
Why Other Options Are Wrong:
If you substitute x = 5, x = 7, or x = 9 into the equation, the left and right sides will not match. For example, for x = 5, left side is 25 − 17 = 8, while right side is −5 + 7 = 2. Hence these values cannot be solutions.
Common Pitfalls:
Typical mistakes include sign errors when moving terms across the equal sign, or incorrect arithmetic when adding or dividing. Some students also try to divide too early without first combining like terms. Proceeding step by step and checking each operation avoids these errors.
Final Answer:
The value of x that satisfies the equation is 4.
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