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Chapter 1: Problem 60

Classify each inequality as either true or false. $$-5 \leq 7$$

Short Answer

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Step by step solution

01

Understand the Inequality

The given inequality is \( -5 \leq 7 \). The symbol \( \leq \) means 'less than or equal to'. Hence, we need to check if -5 is indeed less than or equal to 7.
02

Compare the Values

Compare the two numbers in the inequality: -5 and 7. Answer the question: Is -5 less than or equal to 7?
03

Determine the Truth

Since -5 is less than 7, the statement \( -5 \leq 7 \) is true.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

inequality symbols
In algebra, inequality symbols are essential in comparing values. These symbols include:
  • < (less than)
  • > (greater than)
  • \(egless than or equal to)
  • \(eg>\) (greater than or equal to)
  • \(eq\) (not equal to).

Each symbol allows us to express different relationships between two values. Knowing these helps in understanding and solving inequalities. For instance, in the inequality -5 \(eg\leq\) 7, the \(egegegegegegeg\) symbol indicates that we are checking if -5 is less than or equal to 7.
comparing values
Comparing values in an inequality involves looking at the relative sizes of the numbers. In the example -5 \(eg\leq\) 7, we compare -5 and 7. To do this, visualize their positions on a number line:
  • -5 is to the left of 0
  • 7 is to the right of 0.


Numbers to the left on the number line are smaller than those to the right. Therefore, -5 is indeed less than 7, satisfying the condition expressed by the inequality symbol. This visual tool can simplify comparing values.
truth value of inequalities
The truth value of an inequality tells us whether the statement is true or false. To determine this, follow these steps:
  • Identify the inequality symbol
  • Compare the two values
  • Decide if the relationship holds true.

In the example -5 \(eg\leq\) 7, we've identified the symbol \(\leq\), meaning 'less than or equal to'.

Comparing -5 and 7 confirms that -5 is less than 7. Hence, the inequality holds true, and we say the truth value of this inequality is true.

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Most popular questions from this chapter

Evaluate. $$ 24 \div t^{3}, \text { for } t=-2 $$

Write an equivalent expression without using grouping symbols. $$ -(9 x+1) $$

Evaluate \(3 x y\) for \(x=2\) and \(y=7\)

Simplify. $$ 12 a^{2}-3 a b+5 b^{2}-5\left(-5 a^{2}+4 a b-6 b^{2}\right) $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{46-(3-8)^{3}}{2\left[35-(18-26)^{2}\right]} $$
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