Question

2(x - 5) = -2 (-x - 4)
Give me an 9th grade written explanation on why there is no solution to this equation

Answer 1

Step 1 — Use the distributive property:
2(x − 5) = −2(−x − 4)
2x − 10 = 2x + 8

Step 2 — Remove the same term from both sides:
Subtract 2x from each side:
−10 = 8

This is a false statement (−10 is not equal to 8). That means no number x can make the original equation true. Another way to see the contradiction is to move everything to one side:
0 = 18
which is impossible.

Reason in words: both sides simplify to expressions with the same x-term (2x) but different constants (−10 and +8). Those two linear expressions are parallel lines (same slope, different intercepts), so they never meet — there is no x where they are equal. Therefore the equation has no solution (solution set = ∅).