Question

Solve 9x - 5 = 9x - 5. How many solutions does the equation have? Show your work.

Answer 1

9514 1404 393

Answer:

  an infinite number

Step-by-step explanation:

Subtract 9x -5 from both sides.

  (9x -5) -(9x -5) = (9x -5) -(9x -5)

  0 = 0

This is true for all values of x. There are an infinite number of solutions.

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Additional comment

When you subtract one side of the equation from the other, there are three possible results:

• ax +b = 0 . . . . (a≠0) one solution (x = -b/a)
• 1 = 0 . . . . . . . . no solutions--not true for any value of the variable
• 0 = 0 . . . . . . . infinite solutions--true for every value of the variable