Problem 4 - Prealgebra

Question

Find the solution of each equation from the list given. $$22+n=41 ; 18,19,20$$

Step-by-Step Solution

Answer

The value of \( n \) is 19.

Step 1: Understanding the problem

We need to find the value of \( n \) in the equation \( 22 + n = 41 \) where possible values for \( n \) are given as 18, 19, and 20.

Step 2: Isolate the variable

Subtract 22 from both sides of the equation: \( 22 + n - 22 = 41 - 22 \). This simplifies to \( n = 19 \).

Step 3: Verify the solution

Substitute \( n = 19 \) back into the original equation to check: \( 22 + 19 = 41 \) which simplifies to \( 41 = 41 \). This confirms that our solution is correct.

Key Concepts

Prealgebra

Prealgebra is a foundational math subject that introduces essential mathematical concepts and skills. It prepares students for the complexities of algebra and higher-level math subjects.

In prealgebra, we encounter equations like the one in our exercise: \( 22 + n = 41 \). These equations include numbers and variables, which are symbols used to represent unknown values. Learning to solve these equations is crucial, as it sets the stage for understanding algebra.

Prealgebra focuses on teaching students how to work with basic arithmetic operations, such as addition, subtraction, multiplication, and division, in the context of equations.

• Understanding number properties and operations
• Identifying patterns and relationships between numbers
• Using problem-solving strategies to find unknown values

By mastering prealgebra, students develop a strong mathematical foundation that supports their problem-solving abilities in future math courses.

Variable Isolation

To solve an equation, one must perform variable isolation. This means making the unknown variable stand alone on one side of the equation, which reveals its value.

In the equation \( 22 + n = 41 \), we want to "unlock" \( n \) from the addition operation. We do this by subtracting 22 from both sides of the equation. This step is known as performing the inverse operation:

• Original equation: \( 22 + n = 41 \)
• Subtract 22: \( 22 + n - 22 = 41 - 22 \)
• Isolated variable: \( n = 19 \)

Performing inverse operations such as addition and subtraction is essential when isolating variables so that you correctly simplify equations and identify the value of unknowns. This process shapes problem-solving skills and deepens understanding of algebraic relationships.

Equation Verification

Once a potential solution is found, it is crucial to verify it. Equation verification ensures that the solution meets the original equation's requirements.

After determining \( n = 19 \), the verification process involves substituting this value back into the original equation \( 22 + n = 41 \).

Check the solution by performing the following steps:

• Substitute the value: \( 22 + 19 = 41 \)
• Verify: the left side of the equation equals the right side, since \( 41 = 41 \)

Verification confirms the solution's accuracy and helps to rectify errors during complex problem-solving. Always remember that verification provides confidence in the answer, reinforcing the understanding that mathematics is logical and reliable.