Simplify each inequality if needed. Then determine whether the statement is true or false. -8 > -|-6|

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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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Concetti chiave

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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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