Question

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

Explanation:

Step1: Simplify both sides fully

Start from the partial solution: $3x - 4 = 3x + 4$
Subtract $3x$ from both sides:
$3x - 3x - 4 = 3x - 3x + 4$

Step2: Evaluate the resulting statement

Simplify the expression:
$-4 = 4$
This is a false, contradictory statement with no variables remaining.

Answer:

The equation has no solution.