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

Question

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

A) one solution
B) no solutions
C) two solutions
D) infinitely many solutions

Answer 1

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

multiply each term by 9
45 + 3x = 3x + 54 + x
x = -9

So obviously one solution,

Answer 2

as written, that simplifies to 5 = 6 + x/9

so clearly just one

Care to add some parentheses to clarify your meaning?

Answer 3

It’s one solution I took the apex quiz

Answer 4

Well, let's see... To find out how many solutions this equation has, we can simplify it first.

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

Let's multiply through by 9 to get rid of those fractions:

45 + 3x = 3x + 54 + x

Now, let's move the like terms to one side:

45 = 54 + x

Subtracting 54 from both sides, we get:

-9 = x

So, it looks like we have one solution: x = -9.

That means the clown car of solutions CANNOT fit, and there aren't infinitely many (nice try, crazy clown crew). We're left with answer choice A) one solution.

Answer 5

To determine the number of solutions for this equation, we need to simplify and solve it step by step.

First, let's simplify the equation by combining like terms:

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

To combine the x/3 and x/9 terms, we need to find a common denominator. In this case, the common denominator is 9. We can rewrite the equation using the common denominator:

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

Next, we can simplify:

5 + (3x/9) = (3x/9) + 6 + (x/9)
5 + (1/3)x = (4/9)x + 6

Now, to isolate the variable, we can subtract (1/3)x from both sides:

5 + (1/3)x - (1/3)x = (4/9)x + 6 - (1/3)x
5 = (4/9)x + 6 - (1/3)x

Let's combine the x terms:

5 = (4/9)x - (1/3)x + 6
5 = [(4/9) - (1/3)]x + 6

To simplify further, we need to find a common denominator for (4/9) and (1/3), which is 9. We can rewrite the equation:

5 = [(4/9) - (3/9)]x + 6
5 = (1/9)x + 6

Now, we'll isolate the variable by subtracting 6 from both sides:

5 - 6 = (1/9)x + 6 - 6
-1 = (1/9)x

To solve for x, we'll multiply both sides by 9:

(-1) * 9 = (1/9)x * 9
-9 = x

So the solution to the equation is x = -9.

Since we found a unique value for x, the number of solutions is one.

Therefore, the correct answer is A) one solution.