Determine whether each statement in Exercises 43–50 is true or false. -13 ≤ -2
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Identify the inequality given: .
Understand the meaning of the inequality symbol , which means 'less than or equal to'.
Compare the two numbers: and .
Recall that on the number line, numbers to the left are smaller than numbers to the right.
Determine if is less than or equal to by considering their positions on the number line.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as '≤' (less than or equal to) and '≥' (greater than or equal to) to indicate how one value compares to another. Understanding how to interpret and manipulate inequalities is essential for solving problems that involve comparisons.
A number line is a visual representation of numbers arranged in order, typically extending infinitely in both directions. It helps in understanding the relative positions of numbers, including negative and positive values. By placing numbers on a number line, one can easily see which numbers are greater or lesser, aiding in the evaluation of inequalities.
True or false statements are assertions that can be evaluated for their validity. In the context of inequalities, determining whether a statement is true or false involves checking if the relationship described holds true when the values are compared. This critical thinking skill is fundamental in mathematics, as it allows for the assessment of claims based on logical reasoning.