Question

jillana begins to solve a linear equation that results in a variable expression set equal to the same variable expression. which is the best interpretation of this solution?

• the equation has one solution: ( x = 0 ).
• the equation has one solution: ( x = 1 ).
• the equation has no solution.
• the equation has infinite solutions.

Explanation:

In linear equations, if we end up with a statement like \( x + 2=x + 2\) (a variable expression equal to the same variable expression), this is an identity. An identity is true for all values of the variable, meaning there are infinite solutions because any value substituted for the variable will satisfy the equation. The other options are incorrect: \(x = 0\) or \(x=1\) would be for a specific solution, and "no solution" is when we get a contradiction like \(1 = 0\).

Answer:

The equation has infinite solutions.