Anna is given the equation 3 + 2x = 2x + 3 The replacement set is {2, 3, 4, 5} Anna says the solution is {3}, but the teacher marked her

Question

Anna is given the equation 3 + 2x = 2x + 3 The replacement set is {2, 3, 4, 5} Anna says the solution is {3}, but the teacher marked her problem incorrect. Explain what the answer should be and why. Why do you think this is?

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    2021-11-26T00:16:03+00:00

    Answer:

    The given equation has infinite number of solutions. This means that any real number can be considered a solution to the given equation.

    Since the given replacement set {2,3,4,5} consists of real numbers, therefore, the whole set is considered as a solution to the given equation.

    This is because, when solving the given equation for x, we will end up with 0 = 0, this means that whatever the value of x is, both sides of the equation will always be equal.

    Explanation:

    To solve for x, we need to isolate the x on one side of the equation.

    This can be done as follows:

    3 + 2x = 2x + 3 (subtract 3 from both sides)

    2x = 2x (subtract 2x from both sides)

    0 = 0

    This means that whatever, the value of x is, both sides of the equation will be equal. This means that all real numbers are considered a solution for this equation.

    Let’s verify this using the given replacement set {2,3,4,5}:

    For x = 2:

    Left hand side: 3 + 2(2) = 3 + 4 = 7

    Right hand side: 2(2) + 3 = 4 + 3 = 7

    Both sides are equal.

    For x = 3:

    Left hand side: 3 + 2(3) = 3 + 6 = 9

    Right hand side: 2(3) + 3 = 6 + 3 = 9

    Both sides are equal.

    For x = 4:

    Left hand side: 3 + 2(4) = 3 + 8 = 11

    Right hand side: 2(4) + 3 = 8 + 3 = 11

    Both sides are equal.

    For x = 5:

    Left hand side: 3 + 2(5) = 3 + 10 = 13

    Right hand side: 2(5) + 3 = 10 + 3 = 13

    Both sides are equal.

    Hope this helps 🙂

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