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Using the equation x+3, write one equation that has one solution, one equation that has no solution, and one equation that has infinitely many solutions

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Answer:

  • one: x+3 = 2x
  • none: x+3 = x
  • infinite: x+3 = x+3

Step-by-step explanation:

A linear equation with variable terms on opposite sides of the equal sign will have one solution when the coefficients of those variables are different.

  x+3 = 2x . . . . has one solution (x=3)

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There will be no solution if the variable terms on opposite sides of the equal sign have the same coefficient, but the constants are different. Such an equation can be reduced to 0 = 1, which cannot be made true by any value of the variable.

  x +3 = x . . . . has no solutions

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There will be an infinite number of solutions if the left side of the equal sign is the same as the right side. Every value of the variable will satisfy the equation.

  x +3 = x +3 . . . . has infinite solutions

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