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

Answer 1

Answer: C : The equation has no solution

Explanation:

Answer 2

Solving an equation means finding the value of x which will make the equation true.

We need to undo whatever is done to x to get it by itself.

`4(x-1)-x = 3(x + 5)-11\\Distributing \; 4 \; and \; 3 \; in \; right \; and \; left \; side \; of \; the \; equation\\\\ 4x-4-x=3x+15-11\\Combine \; like \; terms\\\\3x-4=3x+4\\Subtract \; 3x \; on \; both \; sides\\\\3x-3x-4=3x-3x+4\\ Combine \; like \; terms\\\\-4=4`

Conclusion:

Since we end up with an equation which is not TRUE, there is NO solution for this equation. If we graph both the equations, they will end up as a parallel lines which will never meet.