Consider the equation 6x +7=3x � 5. Which of the following possible first steps would prevent having to deal with fractions when solving the

Consider the equation 6x +7=3x � 5. Which of the following possible first steps would prevent having to deal with fractions when solving the equation?

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  1. Answer:

    D.  I or II only

    Step-by-step explanation:

    By a small online search, I’ve found that the equation is:

    6x + 7 = 3x – 5

    And the options are:

    I. Combining the 6x and 3x terms

    II. Combining the 7 and 5

    III. Dividing both sides of the equation  by 6

    A.  I only

    B.  II only

    C.  III only

    D.  I or II only

    E.   I or II or III

    So, let’s solve the equation in such a way that we can prevent the use of fractions:

    6x + 7 = 3x – 5

    We can use I and II, combining one in each side, so we get (so we use I and II at the same time)

    6x – 3x = -5 – 7

    solving these, we get:

    (6 – 3)*x = -12

    3*x = -12

    and -12 is divisible by 3, so if we divide in both sides by 3, we get:

    x = -12/3 = -4

    x = -4

    So we avoided working with fractions, and we used I and II.

    Then the first step could be either I or II (the order does not matter)

    Then the correct option is:

    D.  I or II only

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