91Ó°ÊÓ

When solving linear equations, one of the critical steps is isolating the variable. This means getting the variable by itself on one side of the equation.
In our exercise, the equation is given as: \(8 + k = -4\). Our goal is to isolate \(k\). To do this, we must remove any other numbers or terms from the side of the equation where \(k\) is located.
We do this by performing operations that will cancel out the other numbers. For instance, to isolate \(k\), we subtract 8 from both sides of the equation. This helps us simplify the equation and get \(k\) alone:
\[ 8 + k - 8 = -4 - 8 \]
which simplifies to:
\[ k = -12 \]
Remember: Always perform the same operation on both sides of the equation. This keeps the equation balanced.

Subtracting integers is a common step in solving linear equations. It’s essential to handle them correctly to find the right solution.
Recall our step where we subtracted 8 from both sides of the equation \(8 + k = -4\):
\[ 8 + k - 8 = -4 - 8 \].
By subtracting 8, we simplify the left side to just \(k\). The right side simplifies to \(-12\), since \(-4 - 8 = -12\).
Understanding subtraction of integers can be easier if we think of it as adding the opposite. For example, subtracting 8 is the same as adding -8:
\[ -4 - 8 = -4 + (-8) = -12 \].
Practicing with integer subtraction helps build confidence and accuracy in solving equations.

After finding a solution to an equation, it’s important to verify that the solution is correct. Verification ensures there are no mistakes and that our answer satisfies the original equation.
In our example, we found that \(k = -12\). To verify, substitute \(-12\) back into the original equation \(8 + k = -4\):
\[ 8 + (-12) = -4 \].
Simplifying this, we get \(-4 = -4\), which is a true statement. Both sides of the equation are equal, confirming that our solution \(k = -12\) is correct.
Verification is a crucial step; it confirms the accuracy of our solution and that no errors were made during the solving process.