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SAT Math - How to find 3[6a - 3(1 - a) - 5(a + 1)] is not equivalent to 24(a - ¹/₂) ?

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In this article, we will explore a SAT Math question that involves identifying which expression is NOT equivalent to a given expression: "Which of the following expressions is NOT equivalent to 3 [6a - 3 (1 - a) - 5 (a + 1)]?" The correct answer is Option B) 24(a - ¹/₂).

By the end of this exploration, you will have a clear understanding of how to identify equivalent expressions, enhancing your performance on the SAT Math section. The SAT Math section assesses your mathematical skills, including your ability to simplify and identify equivalent expressions. Recognizing equivalent expressions is essential not only for the SAT but also for solving mathematical problems in various contexts.

Question: Identifying Non-Equivalent Expressions

Question: Which of the following expressions is NOT equivalent to 3 [6a - 3 (1 - a) - 5 (a + 1)]?

Options:

A) 12a - 24

B) 24(a - ¹/₂)

C) 12(a - 2)

D) 24(¹/₂a - 1)

Correct Answer: Option B) 24(a - ¹/₂)

To identify the expression that is NOT equivalent to the given expression, follow these steps:

Step 1: Start with the original expression:

3 [6a - 3 (1 - a) - 5 (a + 1)]

Step 2: Simplify the expression within the brackets:

3 [6a - 3 + 3a - 5a - 5]

Step 3: Continue simplifying:

3 [6a + 3a - 5a - 3 - 5]

Step 4: Combine like terms:

3 [4a - 8]

Step 5: Distribute the 3 outside the brackets:

12a - 24

Step 6: The simplified expression is 12a - 24.

Step 7: Now, compare this with the options to identify the expression that is NOT equivalent.

Step 8: The correct answer is Option B) 24(a - ¹/₂).

Explanation and Key Concepts:

Identifying equivalent expressions involves simplifying the given expression and then comparing it with the options to see which one matches. Each option should produce the same simplified expression as the original for it to be considered equivalent. If one of the options does not match the simplified expression of the original, it is the correct answer for the "NOT equivalent" question.

Recognizing equivalent expressions is a valuable skill for the SAT Math section and mathematics in general. This skill allows you to simplify complex expressions and determine whether different forms are equivalent. By mastering this skill, you'll not only excel on the SAT but also enhance your overall mathematical proficiency.

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