Rationale
x equals 1.
To solve the equation 4 + x = 6 - x, we can isolate x by first adding x to both sides, resulting in 4 + 2x = 6. Then, subtracting 4 from both sides gives 2x = 2, leading to x = 1 when divided by 2.
A) 0
If x were 0, the left side of the equation would equal 4, and the right side would equal 6, making the equation unbalanced. Thus, x cannot be 0 as it does not satisfy the equation.
B) 1
This is the correct answer. Substituting 1 into the original equation results in 4 + 1 = 6 - 1, which simplifies to 5 = 5, confirming that x = 1 satisfies the equation.
C) 2
If x were 2, substituting it into the equation gives 4 + 2 = 6 - 2, resulting in 6 = 4, which is false. Therefore, x cannot be 2 as it does not hold true in the equation.
D) 5
Substituting 5 into the original equation yields 4 + 5 = 6 - 5, which simplifies to 9 = 1, a clear contradiction. Hence, x cannot be 5 as it does not satisfy the equation.
Conclusion
To determine the value of x in the equation 4 + x = 6 - x, the only solution that maintains equality is x = 1. All other choices fail to satisfy the equation, demonstrating that the correct answer is indeed 1.
