Problem 2 - Prealgebra

Question

Find the solution of each equation from the list given. $$13-m=4 ; 7,8,9$$

Step-by-Step Solution

Answer

The solution is \(m = 9\).

Step 1: Understand the Equation

We have the equation \(13 - m = 4\), where we need to find the value of \(m\) that satisfies the equation.

Step 2: Identify the Target Value

The equation is given as \(13 - m = 4\). We need \(13 - m\) to equal 4.

Step 3: Isolate the Variable

To isolate \(m\), subtract 13 from both sides of the equation, giving us \(-m = 4 - 13\).

Step 4: Simplify the Equation

Simplifying the right-hand side, we have \(-m = -9\).

Step 5: Solve for the Variable

Since \(-m = -9\), multiply both sides by -1 to find \(m = 9\).

Step 6: Verify the Solution

Substitute \(m = 9\) back into the original equation: \(13 - 9 = 4\), which confirms the solution is correct.

Key Concepts

Prealgebra

Prealgebra is the foundation upon which algebra skills are built. It helps you understand basic mathematical concepts in a seamless way. In prealgebra, you learn to handle numbers and operations without diving into complex algebraic expressions. It is crucial for developing the skills needed to tackle equations and inequalities later on.

Understanding numbers and their properties is a big part of prealgebra. You start working with whole numbers, fractions, decimals, and simple percentages. At this stage, you also learn the four basic arithmetic operations: addition, subtraction, multiplication, and division.

Prealgebra isn't just about numbers. You also start to encounter concepts like variables, which are symbols that stand for numbers. This is the first step in learning how to deal with equations. By becoming familiar with variables early on, you prepare yourself for solving algebraic equations more comfortably.

Understanding Equations

Equations are like mathematical statements that declare two expressions are equal, often linked by the "=" sign. In prealgebra, understanding equations is crucial. They represent relationships between numbers or variables. When solving an equation, your goal is to find the value of the variable that makes the equation true.

Let's examine the concept using our example equation: \(13 - m = 4\). Here, the equation shows a relationship between 13, some unknown number \(m\), and the number 4.

When approaching equations, follow these steps:

• Identify the variable and understand what the equation is asking you to solve for.
• Look at both sides of the equation to understand how the variable affects the values.
• Consider the operations involved (addition, subtraction) and plan the steps to isolate the variable.

Understanding these steps helps in grasping the essence of how equations work and the logic behind solving them.

Variable Isolation

Variable isolation is a key step in solving equations. It means rearranging the equation so that the variable on one side stands alone. This lets you determine its value. Think of it like peeling away layers of an onion, working towards the core.

Here's how it worked in our example \(13 - m = 4\):

• First, subtract 13 from both sides to simplify the terms and keep the equation balanced.
• This leads to \(-m = -9\).

Once you've simplified, the next step involves getting \(m\) by itself. Since \(-m = -9\), multiply both sides by -1 to isolate \(m\), giving \(m = 9\).

By isolating the variable correctly, you solve the equation. It is essential to perform operations uniformly on both sides ensuring the balance of the equation is maintained. Practice makes this process intuitive, paving the way towards mastering algebra.