# Grade 12 statistics: What is the range of 3x + 2 where 3 ≤ x ≤ 10?

## Question

Here is the question : GRADE 12 STATISTICS: WHAT IS THE RANGE OF 3X + 2 WHERE 3 ≤ X ≤ 10?

## Option

Here is the option for the question :

• 15
• 19
• 20
• 21

And, the answer for the the question is :

21

## Explanation:

Students learn how to find the range of an equation by subtraction the lowest value from the greatest in statistics, which is frequently taught as a pre-college course.

In Grade 12 statistics, understanding the concept of range is essential when analyzing data sets and evaluating the spread of values. Let’s explore the range of the expression 3x + 2, where x is bound within the range of 3 to 10. By applying the principles of algebra and mathematical reasoning, we can determine that the range of 3x + 2, when 3 ≤ x ≤ 10, is 21.

To calculate the range of an expression, we must first understand what it represents. In statistics, the range refers to the difference between the highest and lowest values in a data set. However, in this case, we are dealing with a mathematical expression rather than a set of values. The expression 3x + 2 represents a linear function, where x is the independent variable and 3x + 2 is the dependent variable.

Given the condition 3 ≤ x ≤ 10, we can determine the lowest and highest possible values of the expression 3x + 2. Let’s start by substituting the lower bound, x = 3, into the expression:

3(3) + 2 = 9 + 2 = 11

Next, we substitute the upper bound, x = 10, into the expression:

3(10) + 2 = 30 + 2 = 32

Now we have the lowest and highest values of the expression 3x + 2 when x is within the range of 3 to 10. The range is calculated by finding the difference between these two values:

32 – 11 = 21

Therefore, the range of the expression 3x + 2, where 3 ≤ x ≤ 10, is 21. This means that the values of 3x + 2, as x varies from 3 to 10, span a range of 21 units.

Understanding the range of mathematical expressions is crucial in various statistical and mathematical applications. It allows us to assess the variability and spread of values within a given range. In the case of the expression 3x + 2, knowing its range provides insights into the possible values it can take when x falls within the specified bounds.

By mastering the concept of range and its application to mathematical expressions, Grade 12 statistics students can enhance their analytical skills and develop a deeper understanding of data analysis. Range, along with other statistical measures, empowers students to interpret and draw meaningful conclusions from data, enabling them to make informed decisions and solve real-world problems.

the range of the expression 3x + 2, where 3 ≤ x ≤ 10, is 21. This range represents the difference between the highest and lowest values the expression can take within the specified range of x. Understanding the concept of range and its application to mathematical expressions is an important skill for Grade 12 statistics students, as it enhances their ability to analyze data sets and make meaningful interpretations. By mastering this concept, students can strengthen their statistical reasoning and problem-solving abilities, enabling them to excel in their academic pursuits and future endeavors.

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