Textbook Question
Simplify each radical. See Example 5. √24
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 67
Use a number line to determine whether each statement is true or false. See Example 6. -6 < -1
Verified step by step guidance1
Understand the inequality: The statement is \(-6 < -1\), which means we want to check if \(-6\) is less than \(-1\).
Recall the number line order: On a number line, numbers increase as you move from left to right. Smaller numbers are to the left, and larger numbers are to the right.
Locate \(-6\) and \(-1\) on the number line: \(-6\) is to the left of \(-1\) because \(-6\) is more negative than \(-1\).
Compare their positions: Since \(-6\) is to the left of \(-1\), it means \(-6\) is less than \(-1\).
Conclude the truth value: Therefore, the statement \(-6 < -1\) is true.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Number Line and Ordering of Real Numbers
A number line visually represents real numbers in increasing order from left to right. Numbers to the left are smaller, and those to the right are larger. Understanding this helps compare values like -6 and -1 by their positions on the line.
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3:31
Introduction to Complex Numbers
Inequality Symbols and Their Meaning
Inequality symbols such as '<' indicate the relative size between two numbers. For example, 'a < b' means 'a' is less than 'b'. Correct interpretation of these symbols is essential to determine the truth of statements involving inequalities.
Recommended video:
5:10Finding the Domain and Range of a Graph
Negative Numbers and Their Comparison
Negative numbers are less than zero, but among them, a number with a larger absolute value is actually smaller. For instance, -6 is less than -1 because it lies further left on the number line, despite 6 being greater than 1 in absolute terms.
Recommended video:
5:02Multiplying Complex Numbers
Related Practice
Textbook Question
Factor each polynomial completely. See Example 6. 8x³y⁴ + 12x²y³ + 36xy⁴
Textbook Question
Graph each function. See Examples 6–8. h(x) = -(x + 1)³
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Textbook Question
Use the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 / 5√2
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Textbook Question
Add or subtract, as indicated. See Example 4. (3x)/(x² + x − 12) − x/(x² − 16) + x
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Textbook Question
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2) (b) ƒ(0) (c) ƒ(1) and (d) ƒ(4). See Example 7(d).
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