if x+ a= b/3x and b does not = 3 then x =?
i cant seem to find a way to seprate the two x's since 3/b is always attached.
subtract (b/3)x from both sides
x- (b/3) x+a=0
x(1-b/3)= -a
x= a/(1-b/3)
i looked at the back of my book and the answer is 3a/b-3
To solve the equation x + a = b/3x when b ≠ 3, you can start by rearranging the equation to isolate the x terms on one side of the equation. Here's the step-by-step solution:
1. Start with the equation x + a = b/3x.
2. To separate the x terms, subtract (b/3)x from both sides of the equation: x - (b/3)x + a = 0.
3. Combine the x terms: (1 - b/3)x + a = 0.
4. Factor out the common factor (1 - b/3): (1 - b/3)(x) + a = 0.
5. Divide both sides of the equation by (1 - b/3): x = -a / (1 - b/3).
So the value of x is x = -a / (1 - b/3).
However, the given answer in the back of your book is different and is x = 3a/b - 3. To verify if this answer is correct, let's substitute x = 3a/b - 3 into the original equation and see if it holds true.
Substituting x = 3a/b - 3 into the equation x + a = b/3x:
3a/b - 3 + a = b/3 * (3a/b - 3).
Simplifying the equation further:
(3a + ab - 3b)/b = (ab - 9b)/(3b).
Cross-multiplying will give:
3a + ab - 3b = ab - 9b.
Combining like terms:
3a - 3b = -9b.
Adding 9b to both sides:
3a - 3b + 9b = 0.
Simplifying the equation:
3a + 6b = 0.
It seems like the given answer, x = 3a/b - 3, doesn't satisfy the original equation. Therefore, the correct solution is x = -a / (1 - b/3).