SAT Math - How to find expression ¹/₂ (2a + 3b + 4c) - ³/₂ (b + 2c) is equivalent to a - c

In this article, we will explore a SAT Math question that involves simplifying an algebraic expression: "Which of the following expressions is equivalent to ¹/₂ (2a + 3b + 4c) - ³/₂ (b + 2c)?" The correct answer is Option D) a - c. By the end of this exploration, you will have a clear understanding of how to simplify and identify equivalent expressions, improving your performance on the SAT Math section.

The SAT Math section evaluates your mathematical skills, including your ability to simplify algebraic expressions and identify equivalent forms. This skill is essential for success not only on the SAT but also in various areas of mathematics and problem-solving.

Question: Simplifying an Algebraic Expression

Question: Which of the following expressions is equivalent to ¹/₂ (2a + 3b + 4c) - ³/₂ (b + 2c)?

Options:

A) a - 3c
B) a + 5c
C) a + c
D) a - c

Correct Answer: Option D) a - c

To simplify the given expression and verify which option is equivalent, follow these steps:

Step 1: Start with the original expression:

¹/₂ (2a + 3b + 4c) - ³/₂ (b + 2c)

Step 2: Distribute the coefficients to each term inside the parentheses:

(¹/₂) × 2a + (¹/₂) × 3b + (¹/₂) × 4c - (³/₂) × (b + 2c)

Step 3: Perform the multiplications:

(a + (³/₂)b + 2c - (³/₂)b - 3c)

Step 4: Combine like terms:

a + 2c - 3c

Step 5: Perform the subtraction:

a - c

Step 6: The simplified expression is a - c.

Step 7: The correct answer is Option D) a - c.

Explanation and Key Concepts:

Simplifying algebraic expressions involves distributing coefficients to each term inside parentheses, performing operations with like terms, and simplifying further. When subtracting terms, remember to apply the subtraction to each term within the parentheses. The equivalent expression should match the original expression for all values of 'a,' 'b,' and 'c,' which confirms that Option D) a - c is the correct answer.

Simplifying algebraic expressions is a fundamental skill for the SAT Math section and beyond. Understanding how to distribute coefficients, combine like terms, and simplify expressions efficiently allows you to identify equivalent forms. This skill is valuable in algebra, calculus, and various STEM fields where mathematical manipulation is essential. By mastering this skill, you'll not only excel on the SAT but also enhance your overall mathematical proficiency.



Popular posts from this blog

How to find derivative of x⁴ - 3x² - 7x + 4√x - 5 ?

Image
  In this article, we will delve into the process of finding the derivative of a polynomial function that includes both traditional polynomial terms and a square root term. Specifically, we will work through the steps to find the derivative of the function f(x) = x⁴ - 3x² - 7x + 4√x - 5. Calculus, a branch of mathematics that explores rates of change and the accumulation of quantities, is an essential tool in various fields, from physics to economics. One fundamental concept in calculus is finding the derivative of a function, which provides information about how the function changes with respect to its independent variable.  Understanding Basic Differentiation Rules Before we tackle the given function, let's review some basic rules of differentiation that will be useful: Power Rule:  The derivative of x^n with respect to x, where n is a constant, is n*x^(n-1). Constant Rule:  The derivative of a constant C (where C is any real number) is 0. Sum/Difference Rule:  The derivative of
Read more

How to find derivative of 4x⁵ - 7x² + 2sin(x) - 4cos(x) - 1 ?

Image
In this article, we will explore the process of finding the derivative of a composite function that includes polynomial terms, sine, and cosine functions. Specifically, we will work through the steps to find the derivative of the function f(x) = 4x⁵ - 7x² + 2sin(x) - 4cos(x) - 1.Calculus, the branch of mathematics that deals with rates of change and accumulation, is a crucial tool in various scientific and engineering disciplines. One of the fundamental concepts in calculus is finding the derivative of a function, which describes how the function's values change as the independent variable changes.  Understanding Basic Differentiation Rules Before we dive into finding the derivative of the given function, let's review some fundamental rules of differentiation that will be essential for our calculations: Power Rule:  The derivative of x^n with respect to x, where n is a constant, is n * x^(n-1). Constant Rule:  The derivative of a constant C (where C is any real number) is 0. Su
Read more

How to find derivative of 3x² + ²⁄ₓ + 7 - 4tax(x) + 5sec(x) ?

Image
  In this article, we will walk through the process of finding the derivative of a function that incorporates polynomial terms, a fractional term, and trigonometric functions. Specifically, we will explore how to find the derivative of the function: f(x) = 3x² + ²⁄ₓ + 7 - 4tan(x) + 5sec(x).  Calculus, a branch of mathematics that explores the concepts of rates of change and accumulation, is a foundational tool in various scientific and engineering fields. Among its essential concepts is finding the derivative of a function, which provides insights into how the function changes concerning its independent variable.  Understanding Basic Differentiation Rules Before we delve into finding the derivative of this complex function, let's review some fundamental rules of differentiation: Power Rule: The derivative of x^n with respect to x, where n is a constant, is n * x^(n-1). Constant Rule: The derivative of a constant C (where C is any real number) is 0. Sum/Difference Rule : The deriv
Read more