write a portfolio for algebraic expressions

Answer 1

Portfolio: Algebraic Expressions

Introduction:

In this portfolio, I will showcase my understanding and skills in working with algebraic expressions. I will demonstrate my ability to simplify expressions, solve equations, and apply algebraic concepts to real-life situations. Throughout the portfolio, I will provide examples and explanations to highlight my proficiency in this area of mathematics.

1. Simplifying Algebraic Expressions:

In this section, I will exhibit my proficiency in simplifying algebraic expressions. I will solve multiple expressions by applying the relevant algebraic rules and properties, such as the distributive property, combining like terms, and using the laws of exponents. I will explain each step in detail to showcase my understanding of the process.

Example:
Simplify the expression: 2(x + 3) - 5(2x - 4)

Solution:
First, distribute 2 to each term inside the parentheses:
2x + 6 - 10x + 20

Next, combine like terms by adding or subtracting coefficients of similar variables:
(2x - 10x) + (6 + 20) = -8x + 26

Therefore, the simplified expression is -8x + 26.

2. Solving Algebraic Equations:

In this section, I will demonstrate my proficiency in solving algebraic equations. I will solve various equations of different complexities by applying the appropriate techniques, such as isolating the variable, using inverse operations, and applying the properties of equality. I will provide explicit step-by-step solutions and explanations to illustrate my problem-solving skills.

Example:
Solve the equation: 3x + 7 = 19

Solution:
To isolate the variable, we need to subtract 7 from both sides of the equation:
3x + 7 - 7 = 19 - 7

This simplifies to:
3x = 12

Next, divide both sides of the equation by 3 to solve for x:
3x/3 = 12/3

This simplifies to:
x = 4

Therefore, the solution to the equation 3x + 7 = 19 is x = 4.

3. Applying Algebraic Concepts in Real-Life Situations:

In this section, I will demonstrate my ability to apply algebraic concepts to real-life situations. I will provide examples of word problems where algebraic expressions are used to model and solve various scenarios. I will explain the process of setting up and solving the equations, and analyze the results to draw meaningful conclusions.

Example:
A car rental company charges $25 per day for a car rental and an additional $0.50 per mile driven. If Sarah rented a car for 3 days and drove 150 miles, how much did she pay?

Solution:
Let's denote the total cost as C, the number of days as d, and the number of miles driven as m. Based on the given information, we can set up the following equation:

C = 25d + 0.50m

Substituting the given values, we have:
C = 25(3) + 0.50(150)
C = 75 + 75
C = 150

Therefore, Sarah paid $150 for the car rental.

Conclusion:

In this portfolio, I have demonstrated my proficiency in working with algebraic expressions. I have showcased my ability to simplify expressions, solve equations, and apply algebraic concepts in real-life situations. My step-by-step solutions and explanations illustrate my understanding of the underlying principles and techniques. Overall, my portfolio reflects my competence in algebraic expressions and my capability to apply them effectively.