Question

when she adds 2 to both sides, the equation 4x = 3x results. which solution will best illustrate what happens to x ?
the equation has infinite solutions.
the equation has one solution: x = 0.
the equation has one solution: x = \frac{4}{3}.
the equation has no solution.

Explanation:

Step1: Analyze the equation \(4x = 3x\)

To solve for \(x\), we can subtract \(3x\) from both sides of the equation.
\[4x - 3x=3x - 3x\]

Step2: Simplify the equation

Simplifying both sides, we get:
\[x = 0\]
This shows that the only value of \(x\) that satisfies the equation \(4x = 3x\) is \(x = 0\). So the equation has one solution, which is \(x = 0\).

Answer:

The equation has one solution: \(x = 0\) (the second option).