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Chapter 1: Problem 47

Write a true sentence using either \(< or >\) $$ -5 \square-11 $$

Short Answer

Expert verified
-5 > -11

Step by step solution

01

Understand the Problem

The goal is to choose the correct inequality symbol (either < or >) to make the sentence true between -5 and -11.
02

Compare the Numbers

Recall that in the number line, numbers to the left are smaller. Since -11 is to the left of -5, -11 is smaller than -5.
03

Choose the Correct Inequality Symbol

Since -5 is greater than -11, we use the '>' symbol. Thus, the true sentence is: t -5 > -11.

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Key Concepts

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

Negative Numbers
Negative numbers are less than zero. They are found to the left of zero on the number line. For example, in the exercise, -5 and -11 are both negative numbers. The larger the absolute value of a negative number, the smaller it is. This means that -11 is smaller than -5 because 11 is bigger than 5. Understanding negative numbers is crucial for solving inequalities and comparing them correctly.
Number Line
A number line is a visual representation of numbers on a straight line. It helps us see the order and spacing of numbers. On a number line:
- Numbers increase as you move to the right
- Numbers decrease as you move to the left
For our exercise, placing -5 and -11 on a number line shows that -11 is to the left of -5. Hence, -11 is smaller. Using a number line can make comparing numbers easier, especially with negative numbers.
Inequality Symbols
Inequality symbols help us compare two values. There are two main symbols used:
- '<' means 'less than'
- '>' means 'greater than'
In the exercise, we needed to choose the correct symbol between -5 and -11. Since -11 is less than -5, we use the '>' symbol, making the sentence: -5 > -11. Understanding how to use inequality symbols is essential for comparing numbers and expressing relationships between them.

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Most popular questions from this chapter

Evaluate. $$ (-x)^{2}-5 x, \text { for } x=-3 $$

Evaluate. $$ -30 \div t(t+4)^{2}, \text { for } t=-6 $$

Simplify. Match the algebraic expression with the equivalent rewritten expression below. Check your answer by calculating the expression by hand and by using a calculator. A) \((5(3-7)+4 \wedge 3) /(-2-3)^{2}\) B) \((5(3-7)+4 \wedge 3) /\left(-2-3^{2}\right)\) C)\((5(3-7)+4) \wedge 3 /-2-3^{2}\) D) \(5(3-7)+4 \wedge 3 /(-2-3)^{2}\) $$ \frac{5(3-7)+4^{3}}{(-2-3)^{2}} $$

Solve. Consider only integer replacements. $$2<|x|<5$$

Simplify. $$ |10(-5)|+1(-1) $$
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