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How many solutions does the equation have? 3(7x + 4 ) - 2x + 8 = 5x + 12

User Sangwook
by
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1 Answer

11 votes
11 votes

Answer:

One solution

Explanation:

Well, let's find out by solving the equation for x and seeing how many possible values there are. Our answer could be no solution, one solution, or infinite solutions. So, let's get started by writing out our equation:

3(7x + 4 ) - 2x + 8 = 5x + 12

First, we'll distribute the 3 onto the values on the left:

3(7x) + 3(4) - 2x + 8 = 5x + 12

21x + 12 - 2x + 8 = 5x + 12

Now, we can combine like terms. They are underlined and boldfaced below:

21x + 12 - 2x + 8 = 5x + 12

21x - 2x + 12 + 8 = 5x + 12

19x + 20 = 5x + 12

Next, let's take away 5x from both sides:

19x - 5x + 20 = 5x - 5x + 12

14x + 20 = 12

Finally, we'll subtract 20 from both sides:

14x + 20 - 20 = 12 - 20

14x = -8

Now, all we have to do is divide both sides by 14.

14x/4 = -8/14

x = -4/7

It looks like there is only one solution for x: -4/7. Hopefully that's helpful!

User Nik Todorov
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3.1k points