Textbook Question
Simplify each inequality if needed. Then determine whether the statement is true or false. 7 ≤ 7
0. Review of College Algebra
Complex Numbers
1:48 minutesProblem 99
Textbook Question
Simplify each inequality if needed. Then determine whether the statement is true or false. -8 > -|-6|
Verified step by step guidance1
Identify the absolute value expression in the inequality: \(-|-6|\). Recall that the absolute value of a number is its distance from zero on the number line, always non-negative.
Calculate the absolute value: \(|-6| = 6\) because the absolute value of -6 is 6.
Substitute the absolute value back into the inequality: \(-8 > -6\).
Compare the two numbers on the number line: \(-8\) and \(-6\). Remember that on the number line, numbers to the right are greater.
Determine if the inequality \(-8 > -6\) is true or false based on their positions on the number line.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |-6| equals 6 because 6 is six units away from zero, regardless of the sign.
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Inequality Symbols and Their Meaning
Inequality symbols like '>' indicate the relative size of two values. The symbol '>' means 'greater than,' so a statement like a > b is true if a is larger than b, and false otherwise.
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Comparing Negative Numbers
When comparing negative numbers, remember that a number with a smaller absolute value is actually greater. For example, -8 is less than -6 because -8 lies further left on the number line.
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