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Which statement describes the solutions of this equation?

Which Statement Describes The Solutions Of This Equation class=

Sagot :

sqdancefan

Answer:

  C.  The equation has two valid solutions

Step-by-step explanation:

A rational equation like this is often solved by "cross-multiplying" to eliminate the fractions. When we do that, we get ...

  4(2x+10) = x(3x+1) . . . . . . . multiply both sides by (3x+1)(2x+10)

  3x² -7x -40 = 0 . . . . . . . . . . rearrange to standard form

  3x² -15x +8x -40 = 0 . . . . . . separate -7 into factors of 3(-40)

  3x(x -5) +8(x -5) = 0 . . . . . factor pairs of terms

  (3x +8)(x -5) = 0 . . . . . . . finish factoring

The zeros of these factors are not zeros of the original denominators, so neither of the solutions these give is extraneous.

  3x +8 = 0   ⇒   x = -8/3

  x -5 = 0   ⇒   x = 5

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