91Ó°ÊÓ

Isolating variables is a crucial step in solving linear equations. It involves rearranging the equation to get the variable on one side by itself. This process often requires performing operations like addition, subtraction, multiplication, or division on both sides of the equation.

For example, in the equation \(-5.2 y - 7 = -22.6\), we first move the constant term \(-7\) to the other side. This helps in isolating the term with the variable \(y\). We do this by adding \7\ to both sides:

\[-5.2 y - 7 + 7 = -22.6 + 7\]

which simplifies to:

\[-5.2 y = -15.6\]

Now, the variable term is isolated, making it easier to solve for \(y\).

Remember, whatever operation you perform on one side of the equation, you must do the same on the other side to maintain equality.

Simplifying equations involves reducing the equation to its simplest form. This can include combining like terms and performing arithmetic operations to make the equation more manageable.

In our example, after isolating \(-5.2 y\), we need to simplify the result further. To do this, we divide both sides of the equation by the coefficient of \(y\), which is \(-5.2\):

\[y = \frac{-15.6}{-5.2}\]

Here, \-15.6\ divided by \-5.2\ simplifies to \[y = 3\]. This simplification helps us find the value of \(y\) in its simplest form.

Always double-check your arithmetic to ensure the equation is fully simplified. Simplifying correctly leads to accurate solutions, which is vital in solving any algebraic problems.

Basic algebra involves understanding and manipulating algebraic expressions and equations using foundational concepts. These can include solving for unknown variables, recognizing arithmetic operations, and using properties of equality.

In our exercise, we applied basic algebra to solve the equation \(-5.2 y - 7 = -22.6\):

• Addition to balance the equation
• Division to isolate and solve for \(y\)
• Simplification to find the final value

By following these steps:

Step 1: Add \7\ to both sides:

\[-5.2 y - 7 + 7 = -22.6 + 7\]

Step 2: Isolate the variable by dividing both sides by \-5.2\:

\[y = \frac{-15.6}{-5.2}\]

Step 3: Simplify the division to get

\[y = 3\].

This approach simplifies complex equations step by step, making algebra problems manageable and solvable.