91Ó°ÊÓ

When solving linear equations, one of the primary techniques you will use is isolating the variable. This means you are trying to get the variable alone on one side of the equation.

Imagine the equation: \ k - 11 = 34.
The goal here is to have 'k' by itself on one side of the equation. To do this, you eliminate the number that is subtracted or added to 'k'.

In our case, we need to get rid of \ -11. This is achieved by performing the opposite mathematical operation. Since -11 is subtracted, you add 11 to both sides of the equation.

This gives us:
\[ k - 11 + 11 = 34 + 11 \]
By isolating the variable, you transform the equation into a simpler one, making it easier to find the value of 'k'.

Adding or subtracting the same number from both sides of an equation is a key technique in solving linear equations. It helps to balance the equation while simplifying it.

Using our example, \ k - 11 = 34, the variable k has the value of 11 subtracted from it. To isolate k, we add 11 to both sides of the equation.

This step looks like:
\[ k - 11 + 11 = 34 + 11 \]
On the left side of the equation, \ -11 and \ +11 cancel each other out, leaving us with k. On the right side, you perform regular addition:
\[ 34 + 11 = 45 \]
Thus, the equation simplifies to:
\[ k = 45 \]
By adding or subtracting the same number from both sides of an equation, we keep the equation balanced and simplify it effectively.

After solving an equation, it's important to verify your solution to ensure it is correct. Verification helps you confirm your answer and catch any mistakes made during calculations.

Suppose we found that \ k = 45. We substitute this value back into the original equation to check if it satisfies the equation.

Our original equation is:
\[ k - 11 = 34 \]
Substitute \ k = 45 back into the equation:
\[ 45 - 11 = 34 \]
Simplifying the left side: \ 34 = 34 \
Since both sides of the equation are equal, our solution \ k = 45 \ is verified to be correct.

Verification is a crucial step that should not be skipped, as it confirms the accuracy of your solution and ensures you fully understand the problem-solving process.