91Ó°ÊÓ

In the first step of solving linear equations, our goal is to isolate the variable (in this case, x). Isolating the variable means getting x by itself on one side of the equation. Let's look at the example:

$$ x + 1.6 = 0 $$

To isolate x, we need to remove 1.6 from the left side. This is done by performing the inverse operation to both sides of the equation. Since 1.6 is being added to x, we need to subtract 1.6 from both sides:
$$ x + 1.6 - 1.6 = 0 - 1.6 $$
This simplifies to:
$$ x = -1.6 $$
By isolating the variable, we have determined that the solution to the equation is $$ x = -1.6 $$.
It is crucial to perform the same operation on both sides of the equation to maintain the equality.

After isolating the variable and finding the solution, the next step is to check if the solution is correct. We do this by substituting the solution back into the original equation.
In our example, we found that $$ x = -1.6 $$. Now, we substitute $$ -1.6 $$ back into the original equation:
$$ -1.6 + 1.6 = 0 $$
Simplifying this, we get:
$$ 0 = 0 $$
Since both sides of the equation are equal, our solution $$ x = -1.6 $$ is verified.
Checking your work helps you confirm that your solution is accurate and that no mistakes were made during the isolation process.

Equation simplification is an essential part of solving linear equations. It involves carrying out basic arithmetic operations to reduce the equation to its simplest form. Let's consider the example:
$$ x + 1.6 = 0 $$
First, we subtract 1.6 from both sides to get the variable x by itself:
$$ x + 1.6 - 1.6 = 0 - 1.6 $$
This simplifies to:
$$ x = -1.6 $$
Notice how simplifying helps us understand and solve the equation step by step.
One might wonder, why we should simplify equations?

• It makes the equation more manageable.
• Simplification helps in accurately finding the solution.
• It allows you to see the relationship between variables and constants clearly.

Remember, simplifying equations is a fundamental skill in algebra. It paves the way for understanding more complex mathematical concepts.