9514 1404 393
Answer:
top down: ∞, 0, 1, 0, ∞
Explanation:
The equation will have infinite solutions when the left side and right side simplify to the same expression. This is the case for the first and last expressions listed.
2(x -5) = 2(x -5) . . . . expressions are already identical
x +2(x -5) = 3(x -2) -4 ⇒ 3x -10 = 3x -10 . . . the same simplified expression
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The equation will have no solutions when the x-coefficients are the same, but there are different added constants.
5(x +4) = 5(x -6) ⇒ x +4 = x -6 . . . not true for any x
4(x -2) = 4(x +2) ⇒ x -2 = x +2 . . . not true for any x
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The equation will have one solution when coefficients of x are different.
5(x +4) = 3(x -6) ⇒ 2x = -38 ⇒ x = -19