# 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. Verity

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