Question

2x-5) = 2(x-5) One Solution Infinitely Many Solutions No Solution 5x + 4) = 5(1-6) 5(x + 4) = 3(x-6) 4x - 2) = 4(x + 2) x + 2(x-5) = 3(x - 2) - 4 b) Intro ✓ Done​

Answer 1

9514 1404 393

Answer:

  top down: ∞, 0, 1, 0, ∞

Step-by-step 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