Which equation has the solution x=7?
The Correct Answer and Explanation is :
To find an equation that has the solution ( x = 7 ), we can create a simple linear equation. One straightforward option is:
[
x – 7 = 0
]
Explanation:
- Understanding the Equation: The equation ( x – 7 = 0 ) is a linear equation. In this case, it directly relates ( x ) to a constant value. To isolate ( x ), we can add 7 to both sides of the equation. This gives us: [
x = 7
] This shows that when ( x ) equals 7, the equation holds true, thereby confirming that 7 is indeed a solution. - Generalizing: The equation ( x – 7 = 0 ) is just one example. We can create many other equations that have the same solution. For instance, we can multiply both sides of the equation by any non-zero constant ( k ): [
k(x – 7) = 0
] Expanding this gives: [
kx – 7k = 0
] Thus, ( kx = 7k ) leads us to ( x = 7 ) when we solve for ( x ). - Other Forms: We can also express equations in different forms that yield the same solution. For example: [
2x – 14 = 0
] Solving this equation involves adding 14 to both sides: [
2x = 14
] Then, dividing by 2: [
x = 7
] - Implications in Algebra: The principle behind finding solutions to equations is critical in algebra. Any equation can be transformed as long as we perform the same operation on both sides, maintaining the equality. This foundational concept allows for the creation of numerous equations with identical solutions, showcasing the versatility of algebraic manipulation.
In summary, the equation ( x – 7 = 0 ) is a simple representation that has the solution ( x = 7 ). By understanding how to manipulate equations, we can generate many others that lead to the same conclusion.