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:

Analyze the given scenario

The problem states that Jillana solves a linear equation and gets a variable expression set equal to the exact same variable expression (for example, \(ax + b = ax + b\)).

Apply mathematical definitions

Using the Linear Equation Identities concept, when an equation simplifies to an identity where both sides are identical, any value substituted for the variable will make the equation true.

Determine the number of solutions

Since the statement is true for all real numbers, the equation has infinitely many solutions.

Answer:

• The equation has one solution: \(x = 0\).
• The equation has one solution: \(x = 1\).
• The equation has no solution.
• The equation has infinite solutions. (Correct answer)