Solve for w.
8-(3/w+1)=(7/w+2)
8-(3/w+1)=(7/w+2)
8 - 3/w - 1 = 7/w + 2
5 = 10/w
multiply by w
5w = 10
w = 2
I don't know if I entered this problem right it falls in the solving rational equation that simplifies to a quadratic equation
To solve for w in the equation 8 - (3/w + 1) = (7/w + 2), we will follow these steps:
Step 1: Simplify both sides of the equation.
Step 2: Move all terms containing w to one side of the equation.
Step 3: Isolate the w term by removing any addition or multiplication operations.
Step 4: Solve for w by finding the common denominator and simplifying the equation.
Step 5: Check the solution by substituting the value of w back into the original equation.
Let's solve the equation step by step:
Step 1: Simplify both sides of the equation.
On the left side, we have 8 - (3/w + 1), which can be rewritten as 8 - (3/w) - 1.
On the right side, we have (7/w) + 2.
So, the equation becomes: 8 - (3/w) - 1 = (7/w) + 2.
Step 2: Move all terms containing w to one side of the equation.
To do this, let's subtract (7/w) and 2 from both sides of the equation.
8 - (3/w) - 1 - 2 = (7/w) + 2 - (7/w) - 2.
After simplification, the equation becomes: 5 - (3/w) = 0.
Step 3: Isolate the w term by removing any addition or multiplication operations.
Let's get rid of the fraction by multiplying both sides of the equation by w.
w * (5 - (3/w)) = w * 0.
This simplifies to: 5w - 3 = 0.
Step 4: Solve for w by finding the common denominator and simplifying the equation.
Now, let's move the constant term, -3, to the other side of the equation by adding 3 to both sides.
5w - 3 + 3 = 0 + 3.
This simplifies to: 5w = 3.
Finally, divide both sides of the equation by 5 to solve for w.
w = 3/5.
Step 5: Check the solution by substituting the value of w back into the original equation.
Substituting w = 3/5 into the original equation:
8 - (3/(3/5) + 1) = (7/(3/5) + 2).
Simplifying further:
8 - (3/(3/5)) - 1 = (7/(3/5)) + 2.
8 - (3*5/3) - 1 = (7*5/3) + 2.
8 - 5 - 1 = 35/3 + 2.
2 = 35/3 + 2.
To compare both sides, let's convert 2 to a fraction:
2 = 6/3.
Now, the equation becomes:
2 = 35/3 + 6/3.
15/3 = 41/3.
Both sides of the equation are equal. Therefore, the solution w = 3/5 satisfies the original equation.
Therefore, the solution for w in the equation 8 - (3/w + 1) = (7/w + 2) is w = 3/5.