2/5+1/y+5=y-7/5y-25
how about some parentheses or spaces? It's not clear just what you mean.
Solve the equation and check your solution 2/5+1/y-5=y-7/5y-25
If you mean
2/5 + 1/(y-5) = (y-7)/(5y-25)
(see how parentheses make it clear?) then we wind up with
2(y-5) + 5 = y-7
y = -2
check:
2/5 - 1/7 = -9/-35
(14-5)/35 = 9/36
yes.
To solve the equation 2/5 + 1/y + 5 = y - 7/5y - 25, we need to first simplify the equation by combining like terms.
The equation can be rewritten as:
2/5 + 1/y + 5 = y - (7/5)y - 25
We need to combine the terms 2/5, 1/y, and 5 on the left side of the equation.
The first step is to find a common denominator for 2/5 and 5, which is 5.
2/5 can be written as 2(1/5), so the common denominator is 5 and it becomes (2/5)(5/5) = 10/25.
So, the equation can be rewritten as:
10/25 + 1/y + 5 = y - (7/5)y - 25
Now, we need to find the common denominator for 1/y and y.
The common denominator in this case is y, so 1/y stays as it is.
The equation becomes:
10/25 + 1/y + 5 = y/y - (7/5)y - 25
Simplifying further, the equation becomes:
10/25 + 1/y + 5 = 1 - 7/5 - 25
To simplify further, we can convert the mixed number 1 - 7/5 into an improper fraction.
1 can be written as 5/5, so the mixed number becomes (5/5) - (7/5) = (5 - 7)/5 = -2/5.
So, the equation now becomes:
10/25 + 1/y + 5 = -2/5 - 25
Next, we can simplify the equation by multiplying all terms by the common denominator to get rid of the denominators.
Multiplying both sides of the equation by 25, we get:
25 * (10/25) + 25 * (1/y) + 25 * 5 = 25 * (-2/5) - 25 * 25
This simplifies to:
10 + 25/y + 125 = -10 - 625
Combining like terms, the equation now becomes:
135 + 25/y = -635
We can then isolate the variable by subtracting 135 from both sides of the equation:
135 + 25/y - 135 = -635 - 135
This simplifies to:
25/y = -770
Now, to solve for y, we can cross multiply:
25 = -770 * y
Dividing both sides of the equation by -770, we get:
y = 25 / -770
Finally, the solution for y is obtained by dividing 25 by -770, which gives:
y = approximately -0.0325