91Ó°ÊÓ

Whenever you encounter a linear equation, your main goal is often to find the value of the unknown variable. This process is known as 'isolating the variable.'
In the equation from the exercise, we have
\[ x - 7 = 18 \]

To isolate the variable (x in this case), you need to perform operations that will leave x by itself on one side of the equation.
In simpler terms, you want to get rid of the -7 next to the x. To do this, you perform the opposite operation. Since -7 is subtracted from x, you'll add 7 to both sides of the equation.
It looks like this:
\[ x - 7 + 7 = 18 + 7 \]
This addition cancels out the -7 on the left, leaving us with:
\[ x = 25 \]
Remember, whatever you do to one side of the equation, you must do to the other to keep the equation balanced. This step is crucial for isolating the variable!

Simplifying an equation means performing all the necessary operations to make the equation as straightforward as possible. This can include combining like terms, reducing fractions, and performing arithmetic operations.
In our equation, we simplified by combining constants after isolating the variable:
\[ x - 7 + 7 = 18 + 7 \]
Quick mental math tells us that
\[ -7 + 7 = 0 \]
and
\[ 18 + 7 = 25 \]
This simplifies our equation to:
\[ x = 25 \]
Now, the equation is as simple as it can get. It tells us outright that the value of x is 25, with no further operations needed. Simplifying helps make the solution clearer and confirms that no errors were made in earlier steps.

Basic algebra is the fundamental toolset used for solving equations like the one in this exercise. Key concepts in basic algebra include understanding variables, constants, and arithmetic operations.
In our example:

- \[ x \] is the variable.
- \[ -7 \] and \[ 18 \] are constants.

The primary operations used here were addition and equality. Here’s the equation again:
\[ x - 7 = 18 \]
To solve this, we know we need to cancel out the -7 by adding 7 to both sides, leading us to:
\[ x - 7 + 7 = 18 + 7 = 25 \]
Understanding these basic operations and concepts is essential in algebra. They form the foundation for more complex mathematical problems you'll encounter later.