Problem 55 - Algebra A Combined Function

Question

\(5-0.3 k=5\)

Step-by-Step Solution

Answer

The solution to the equation is \(k = 0\).

Step 1: Understand the Equation

The given equation is \(5 - 0.3k = 5\). Our goal is to find the value of \(k\), which will satisfy this equation.

Step 2: Isolate the Variable

To find \(k\), we should first isolate the term involving \(k\). We can start by subtracting 5 from both sides of the equation, resulting in \(-0.3k = 0\).

Step 3: Solve for the Variable

Next, divide both sides of the equation by \(-0.3\) to solve for \(k\). This gives us \(k = \frac{0}{-0.3}\), which simplifies to \(k = 0\).

Key Concepts

Variables

In algebra, a variable is a symbol that represents an unknown number, making it possible to express mathematical ideas in a flexible way. In the equation \(5 - 0.3k = 5\), the variable is \(k\). This symbol stands in for a number we do not yet know and need to find. Understanding that variables can change or represent different values depending on the equation is fundamental.

• Variables are crucial because they allow us to create general rules or formulas that work across numerous situations.
• They act as placeholders for numbers in equations and expressions.

In our exercise, isolating \(k\) will let us find the specific value that makes the equation true. Knowing how to manage and solve for variables is key to solving any algebraic equation.

Equation Isolation

Equation isolation refers to the process of rearranging an equation so that the variable you want to solve for is by itself on one side of the equation. In our example, we want to isolate \(k\) in the equation \(5 - 0.3k = 5\).

To achieve isolation:

• Subtract 5 from both sides, which gives \(-0.3k = 0\).

It's important to perform the same operation on both sides of the equation to keep the equation balanced.

Here are some general tips:

• Identify the term with the variable.
• Use addition, subtraction, multiplication, or division to get the variable by itself.

Isolation of the variable is the first big step toward finding its value, setting us up perfectly to solve for it in the next step.

Equation Simplification

Once the variable is isolated, we need to simplify the equation to solve for the variable. In this context, simplifying often means breaking down complex parts of the equation by performing operations on them. With our simplified equation \(-0.3k = 0\), the task is to make \(k\) explicit.

Here is how simplification works in our example:

• Divide both sides by \-0.3\ to solve for \(k\), resulting in \(k = \frac{0}{-0.3}\).
• This simplifies to \(k = 0\).

Simplification helps us reach the simplest form of an equation where the solution is visible.

Each step in equation simplification not only brings us closer to the solution but helps to ensure our final answer is accurate and in its simplest form.