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: $x = 8$. the equation has infinite solutions. the equation has one solution: $x = 0$. the equation has no solution.

Explanation:

Step1: Analyze the final equation

We have the equation \(3x - 4=3x + 4\). Let's try to solve for \(x\) by subtracting \(3x\) from both sides.
\(3x-4 - 3x=3x + 4-3x\)

Step2: Simplify both sides

Simplifying the left - hand side: \(3x-3x - 4=-4\)
Simplifying the right - hand side: \(3x - 3x+4 = 4\)
So we get \(-4 = 4\), which is a false statement. When we end up with a false statement after trying to solve a linear equation, it means that there are no values of \(x\) that will satisfy the original equation.

Answer:

The equation has no solution.