Solving the Equation (y 11)/6-(y 1)/9=(y 7)/4:

To find the value of y that satisfies the equation (y 11)/6-(y 1)/9=(y 7)/4, we can use the following steps:

Step 1: Simplify the Equation

We can simplify the equation by multiplying both sides by the least common multiple of the denominators, which is 36. This gives us:

9(y + 11) - 4(y + 1) = 27(y + 7)

Simplifying this equation gives us:

9y + 99 - 4y - 4 = 27y + 189

5y + 95 = 27y + 189

Step 2: Solve for y

We can solve for y by subtracting 5y from both sides and subtracting 95 from both sides. This gives us:

22y = 94

y = 94/22 = 47/11

Therefore, the value of y that satisfies the equation (y 11)/6-(y 1)/9=(y 7)/4 is y = 47/11.

Explanation:

When solving an equation, it is important to simplify it as much as possible before trying to solve for the variable. In this case, we simplified the equation by multiplying both sides by the least common multiple of the denominators. This allowed us to eliminate the fractions and work with whole numbers.

Once we had a simplified equation, we could solve for y by isolating the variable on one side of the equation. We did this by subtracting 5y from both sides and subtracting 95 from both sides. This gave us a single value for y that satisfies the equation.

It is important to check our answer by plugging it back into the original equation and verifying that both sides are equal. If they are, then we have found the correct value for y.