91Ó°ÊÓ

The first step in solving any linear equation is to isolate the variable you are solving for. In our case, we need to solve for \(y\) in the equation \(y - 7.82 = -16\). To do this, we need to move the constant term (which is -7.82) from one side of the equation to the other. This action simplifies our equation and isolates \(y\) on one side.

To move the -7.82 to the other side, we perform the operation of adding 7.82 to both sides of the equation:

y - 7.82 + 7.82 = -16 + 7.82
This operation eliminates the -7.82 on the left side and simplifies to:

y = -16 + 7.82
Now, our equation is simpler and we have isolated the variable \(y\). This prepares us for the next step: performing the addition.

Once we have the variable isolated, the next step is performing the necessary arithmetic operations to solve for it. In our current equation, we need to calculate the expression \(-16 + 7.82\).

To do this addition, follow these steps:

• Recognize that -16 and 7.82 have opposite signs; thus, we are essentially performing a subtraction.
• Find the difference between the two numbers: \|16 - 7.82\| = 8.18.
• Determine the sign of the result by looking at the numbers involved. Here, because -16 has a larger absolute value, our result will be negative.

Combining these steps, we get:

y = -8.18
Now, we have found the value of \(y\), which is -8.18.

Our final step is to verify that our solution is correct. Verification involves substituting the found value back into the original equation to see if both sides equal each other.

In our case, we substitute \(y = -8.18\) back into the original equation \(y - 7.82 = -16\):

y - 7.82 = -16
Now substitute \( y = -8.18\):

-8.18 - 7.82 = -16
Perform the subtraction on the left side:

-16 = -16
Since both sides are equal, it confirms that our solution is correct. This verification step is crucial in ensuring that you have solved the equation properly and that no errors were made during calculations.