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

Question

mr Goodwill

3 months ago

15

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

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-02-27T18:26:02+03:00

Finding a solution to an equation entails determining the value of x that renders the equation valid.

We must reverse the operations applied to x to isolate it.

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

Final Note:

The resulting equation is false, indicating that there is NO solution. Graphically, both equations will be represented as parallel lines that do not intersect.

AnnZ [12.3K] · Answer 2 · 2026-02-27T18:28:10+03:00

Conclusion:

Final determination: No solution exists for this equation.

Detailed Explanation:

4 (x - 1) - x = 3 (x + 5) - 11, the solving process would involve: 4x - 4 - x = 3x + 15 - 11; 3x - 4 = 3x + 4. While the steps seem appropriate, continuity leads to the cancellation of x, confirming that there is no solution as no value for x can satisfy the equation, represented graphically as two parallel lines that never intersect.

Final determination: No solution exists for this equation.