91Ó°ÊÓ

Prealgebra is the foundation of mathematics that prepares students for algebra. It involves basic arithmetic and introduces concepts such as variables and simple equations. Understanding prealgebra is crucial because it's the building block for more complex math topics.

In prealgebra, you often work with whole numbers, fractions, and decimals. It sets the stage for learning how to solve equations, which is a key algebraic skill.

• Focus on arithmetic with variables.
• Transitions from arithmetic operations to algebraic thinking.
• Introduces the concept of balancing equations.

For example, in the given equation, we are tasked with solving for a variable, which is a common prealgebra exercise. By understanding and practicing these types of problems, students gain confidence and skills needed for tackling algebra.

Isolating the variable is a crucial step in solving equations. It means getting the unknown variable by itself on one side of the equation. This process helps us to find the value of the variable that makes the equation true.

To isolate the variable, you often perform operations that "undo" what is being done to the variable. For the equation given, 3r + 4 = 19, the term 3r is isolated by first removing the constant term 4. You do this by subtracting 4 from both sides of the equation:

• Subtract 4 from both sides: \(3r + 4 - 4 = 19 - 4\)
• This results in: \(3r = 15\)

Once 3r is isolated, the next step is to solve the simpler equation \(3r = 15\) by division.
Isolating the variable makes the problem easier to solve and understand, leading to the solution for r. Remember, whatever you do to one side of the equation, you must also do to the other to keep it balanced.

A step-by-step solution helps break down the process of solving an equation into manageable parts. This method allows students to follow a logical sequence and understand each action leading to the final answer.

Here's a step-by-step breakdown of solving \(3r + 4 = 19\):

• Step 1: Isolate the variable term. Subtract 4 from both sides to eliminate the constant term:
  \(3r + 4 - 4 = 19 - 4\), which simplifies to \(3r = 15\).
• Step 2: Solve for the variable. Divide both sides by 3 to solve for r:
  \(\frac{3r}{3} = \frac{15}{3}\), resulting in \(r = 5\).

By following these steps, students learn the systematic process of solving equations. The clarity of a step-by-step solution builds both understanding and confidence in handling equations.