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.