Difficulty: Easy
Correct Answer: 4
Explanation:
Introduction / Context:
This question is a straightforward linear equation in one variable. It checks basic algebra skills, such as combining like terms and isolating the variable x. Such questions are common in aptitude and entrance tests because they quickly reveal whether a candidate is comfortable manipulating simple equations.
Given Data / Assumptions:
We are given the equation 5x − 17 = −x + 7.The unknown variable is x.All operations are over real numbers.
Concept / Approach:
The standard procedure for solving a linear equation is to bring all terms containing x to one side of the equation and constants to the other side. After that, we simplify and divide by the coefficient of x to find its value. Careful handling of negative signs is important to avoid arithmetic errors.
Step-by-Step Solution:
Step 1: Start from 5x − 17 = −x + 7.Step 2: Add x to both sides to collect x terms on the left: 5x + x − 17 = 7.Step 3: Simplify the x terms: 6x − 17 = 7.Step 4: Add 17 to both sides to move the constant: 6x = 7 + 17.Step 5: Compute the sum on the right: 6x = 24.Step 6: Divide both sides by 6: x = 24 / 6.Step 7: Simplify the fraction: x = 4.
Verification / Alternative check:
Substitute x = 4 back into the original equation. The left hand side becomes 5 * 4 − 17 = 20 − 17 = 3. The right hand side becomes −4 + 7 = 3. Since both sides are equal, the equation is satisfied for x = 4. This confirms that the solution is correct.
Why Other Options Are Wrong:
If x = 5, then 5x − 17 = 25 − 17 = 8 while −x + 7 = −5 + 7 = 2, which do not match. If x = 7, then 5x − 17 = 35 − 17 = 18 while −x + 7 = −7 + 7 = 0, again not equal. If x = 9, then 5x − 17 = 45 − 17 = 28 while −x + 7 = −9 + 7 = −2, which also does not satisfy the equation. Therefore only x = 4 works.
Common Pitfalls:
Learners sometimes subtract x from 5x incorrectly or mis-handle the constant term when moving it from one side to the other. Forgetting to perform the same operation on both sides of the equation is another common error. Double checking each step and performing a quick substitution at the end helps avoid these mistakes.
Final Answer:
The value of x that satisfies 5x − 17 = −x + 7 is 4.
Discussion & Comments