Textbook Question
Add or subtract, as indicated. See Example 6. √6 + √6
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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 89
Simplify each inequality if needed. Then determine whether the statement is true or false. 0 ≤ -5
Verified step by step guidance1
First, understand the inequality given: \(0 \leq -5\) means "0 is less than or equal to -5."
Recall the number line order: numbers increase as you move to the right. Zero is to the right of -5, so 0 is greater than -5.
Since 0 is greater than -5, the statement \(0 \leq -5\) is not true.
Therefore, the inequality cannot be simplified further because it is already in its simplest form.
Conclude that the statement \(0 \leq -5\) is false.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Understanding Inequalities
Inequalities compare two values or expressions, indicating if one is less than, greater than, or equal to the other. They can be simplified or manipulated similarly to equations, but special care is needed when multiplying or dividing by negative numbers, as this reverses the inequality sign.
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Finding the Domain and Range of a Graph
Evaluating Inequality Statements
To determine if an inequality is true or false, substitute or analyze the values on both sides. For example, checking if 0 ≤ -5 involves comparing zero and negative five directly, understanding their positions on the number line.
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7:28Evaluate Composite Functions - Values Not on Unit Circle
Number Line and Order of Real Numbers
The number line visually represents real numbers in increasing order from left to right. Knowing that zero is greater than any negative number helps quickly assess inequalities like 0 ≤ -5, since zero lies to the right of -5, making the statement false.
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3:31Introduction to Complex Numbers
Related Practice
Textbook Question
Add or subtract, as indicated. See Example 6. 5√3 - √3
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Textbook Question
Factor each polynomial completely. See Example 6. 8t³ + 125
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Textbook Question
Simplify each complex fraction. See Examples 5 and 6. (1/(x + 1) − 1/x) / (1/x)
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Textbook Question
Use an inequality symbol to write each statement. 5 + 0 is not equal to 0.
Textbook Question
Simplify each inequality if needed. Then determine whether the statement is true or false. 7 ≤ 7
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