One Solution, No Solutions, Infinite Solutions- Open Middle Problem

Using Integers (without repeating any number),  fill in the boxes to create the following types of Linear Equations:

Linear Equation with one solution:

Equations

Linear Equation with no solutions:

 Equations

Linear Equation with infinite solutions:

Equations

What is the smallest Integer interval that could produce all three equations?

3 thoughts on “One Solution, No Solutions, Infinite Solutions- Open Middle Problem

  1. J S says:

    The question “What is the smallest integer interval that could produce all three equations?” seems non-intuitive. Clearly all of the equations could have essentially limitless answers so there won’t be one “right” answer, but what do you mean by “the smallest integer interval”, are you referencing the interval between the highest and lowest integers used among all three equations? Are you referencing the smallest possible value of integers that you can use to construct three equations of this type? Are you referencing the value of X (which can only be the answer to the first question as it’s X value would work in the equation that provides infinite solutions and no X value would ever result in a solution in the middle equation answer)? You put a sample answer on another site as:

    1 Solution: (-3/-1)X + 0 = 1X + (-4/-2)
    No Solution: (-2/-1)X + 1 = 2X + 0
    Infinite Solutions: (-2/-1)X + 3 = 2X + (-9/-3)

    Interval of: 11

    How do you come up with that interval? The spread or interval between the highest and lowest integer used in the three equations here is 12 (3 to -9), not 11. The “1 solution” sample answer must have a value for X of 1, so the interval cannot be the value of X. I’m a bit confused here (obviously).

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