Question

How many Solutions does 6 + x/5 = x/5 - 5 - 3x/10 have?

Answer 1

9514 1404 393

Answer:

  1 solution (x = -36 2/3)

Step-by-step explanation:

  6 + x/5 = x/5 - 5 - 3x/10 . . . . . . . given

  60 +2x = 2x -50 -3x . . . . . . . . . multiply by 10

  3x = -110 . . . . . . . . . . . . . . . .  add x-60 to both sides

  x = -110/3 = -36 2/3 . . . . . .divide by the coefficient of x

There is one solution to the equation.

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Additional comment

The coefficient of x on the left side of the equation is not equal to the coefficient of x on the right side. When that is the case, the equation will have one solution.

When the coefficients are equal, there will be no solutions if the constants are different, and there will be infinite solutions if the constants are the same.