91Ó°ÊÓ

Isolating variables is a key concept in solving linear equations. When we talk about isolating variables, we're essentially discussing how to get the variable (usually represented as x) by itself on one side of the equation. This approach simplifies the equation and makes it easier to solve for the unknown.

In our exercise, we started with the function: \[ f(x) = 0.5 - x \]
To find the zeros, we set the function equal to zero and got: \[ 0.5 - x = 0 \]
The next step involves isolating the variable x. To do that, we added x to both sides: \[ 0.5 - x + x = 0 + x \]
This simplifies to: \[ 0.5 = x \]
Notice how our aim is to get x by itself. By performing the same operation (adding x) on both sides of the equation, we ensure that we maintain balance and simplify the equation to isolate x.

Linear equations are mathematical statements of equality involving constants and variables. The general form of a linear equation in one variable is usually written as: \[ ax + b = 0 \] where a and b are constants, and x is the variable.

In our exercise, we were given: \[ f(x)=0.5 - x \]
This is a linear equation since it can be rewritten in the form of \[ -x + 0.5 = 0 \] which is the same as the general form with \[ a = -1 \] and \[ b = 0.5 \].

To solve linear equations, you follow these steps:

• Collect all terms involving the variable on one side of the equation.
• Collect all constant terms on the opposite side of the equation.
• Isolate the variable through division or multiplication, if necessary.

Applying this to our function, we obtained the solution \[ x = 0.5 \].

Solving equations involves finding the unknown value that makes the equation true. For linear equations, this process is typically straightforward.

In our provided exercise and solution:

• First, we set the function equal to zero: \[ 0.5 - x = 0 \].
• Then, we isolated the variable x by adding x to both sides: \[ 0.5 - x + x = 0 + x \].
• This gave us: \[ 0.5 = x \].

The value of x we obtained, \[ x = 0.5 \], is the zero of the function.

Let’s summarize simple steps to solve linear equations:

• Set the function equal to zero.
• Isolate the variable.
• Perform operations to simplify and solve for the unknown variable.

By practicing these steps, solving linear equations like this will become second nature!