7y+2 upon 5=6y-5 upon 11 solve the following and verify the solution

To solve the equation \(\frac{7y + 2}{5} = \frac{6y - 5}{11}\), we'll follow these steps:

### Step 1: Cross Multiply
We'll start by cross multiplying to eliminate the fractions:

\[
(7y + 2) \times 11 = (6y - 5) \times 5
\]

### Step 2: Expand Both Sides
Now, expand both sides of the equation:

\[
11 \times 7y + 11 \times 2 = 5 \times 6y - 5 \times 5
\]

This simplifies to:

\[
77y + 22 = 30y - 25
\]

### Step 3: Bring Like Terms Together
Next, we'll move all the terms involving \(y\) to one side and constant terms to the other side:

\[
77y - 30y = -25 - 22
\]

This simplifies to:

\[
47y = -47
\]

### Step 4: Solve for \(y\)
Now, divide both sides by 47 to find the value of \(y\):

\[
y = \frac{-47}{47} = -1
\]

### Step 5: Verify the Solution
To verify, substitute \(y = -1\) back into the original equation:

Original equation:
\[
\frac{7y + 2}{5} = \frac{6y - 5}{11}
\]

Substitute \(y = -1\):
\[
\frac{7(-1) + 2}{5} = \frac{6(-1) - 5}{11}
\]

Simplify both sides:
\[
\frac{-7 + 2}{5} = \frac{-6 - 5}{11}
\]
\[
\frac{-5}{5} = \frac{-11}{11}
\]

Both sides simplify to:
\[
-1 = -1
\]

Since both sides are equal, the solution \(y = -1\) is verified.

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. What happens if you solve the equation using substitution instead of cross multiplication?
2. How do you solve a similar equation with different coefficients?
3. What are the implications of a negative solution in real-world scenarios?
4. How would the solution change if the equation were an inequality?
5. How can you check for extraneous solutions when solving equations?

**Tip:** Always verify your solution by substituting it back into the original equation to ensure accuracy.

Learn how to solve the equation (7y + 2)/5 = (6y - 5)/11 with a detailed step-by-step solution. This problem involves cross multiplication and fraction simplification. Suitable for high school students.

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