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9 votes
9 votes
How many solutions does 5 + x/3 = x/3 + 6 + x/9

A. Infinitely many solutions
B. Two solutions
C. No solutions
D. One solution

User John Kuriakose
by
3.0k points

1 Answer

13 votes
13 votes

Answer: D) one solution

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Step-by-step explanation:

A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation

5 = 6 + (x/9)

Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1

Then plug in w = x/9 and solve for x.

w = -1

x/9 = -1

x = 9*(-1)

x = -9

We get exactly one solution and it is x = -9

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Check:

5 + x/3 = x/3 + 6 + x/9

5 + (-9)/3 = (-9)/3 + 6 + (-9)/9

5 - 3 = -3 + 6 - 1

2 = 3 - 1

2 = 2

We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.

User DimanNe
by
3.3k points