Question

lily begins solving the equation $4(x - 1) - x = 3(x + 5) - 11$. her work is shown here.
students work
$4(x - 1) - x = 3(x + 5) - 11$
$4x - 4 - x = 3x + 15 - 11$
$3x - 4 = 3x + 4$
how can her partial solution be interpreted?
the equation has one solution: $x = 0$.
the equation has one solution: $x = 8$.
the equation has infinite solutions.
the equation has no solution.

Explanation:

Step1: Analyze the equation

We have the equation \(3x - 4=3x + 4\).

Step2: Subtract \(3x\) from both sides

Subtracting \(3x\) from both sides gives \(- 4 = 4\), which is a false statement.

Step3: Determine the number of solutions

Since we end up with a false statement (\(-4 = 4\) is not true), the equation has no solution.

Answer:

The equation has no solution.