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Chapter 2: Problem 68

To prepare for Section \(2.6,\) review inequalities. Write a true sentence using either \(<\) or \(>\) $$-9 \square-12$$

Short Answer

Expert verified
-9 > -12.

Step by step solution

01

- Understand the inequality symbols

The symbol '<' means 'less than' and the symbol '>' means 'greater than'. We need to determine whether -9 is less than or greater than -12.
02

- Compare the numbers

When comparing two negative numbers, the number with the smaller absolute value is actually greater. For example, -9 has a smaller absolute value compared to -12.
03

- Write the true sentence

Since -9 is greater than -12, the correct inequality is $$-9 > -12$$

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Key Concepts

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

inequality symbols
Understanding how to use inequality symbols is crucial in algebra and everyday math.
The two main inequality symbols are '<' and '>'.
  • The symbol '<' means 'less than.'
  • The symbol '>' means 'greater than.'
For instance, if we write 3 < 5, it means that 3 is less than 5.
Similarly, 8 > 4 means that 8 is greater than 4.
It's important to know how to interpret and use these symbols correctly to solve inequality problems.
In the exercise given, we need to figure out whether -9 is less than or greater than -12.
negative numbers
Negative numbers can be tricky, but with a bit of practice, they become easier to understand.
Negative numbers are numbers less than zero.
They are denoted with a minus sign (-) in front.
For example, -3, -7, and -12 are all negative numbers.
When comparing negative numbers, remember that the number with the smaller absolute value is actually greater.
The absolute value of a number is its distance from zero on a number line, without considering direction.
For instance, the absolute value of -5 is 5.
So, in comparing -9 and -12, -9 has an absolute value of 9 and -12 has an absolute value of 12.
Since 9 is less than 12, -9 is actually greater than -12.
comparing numbers
Comparing numbers, especially negative numbers, can be made easier by thinking of their positions on a number line.
On a number line, numbers to the left are always less than numbers to the right.
For example, -12 is to the left of -9 on the number line, thus, -12 is less than -9.
When we put this into the form of an inequality, we say -9 > -12.
It might feel a bit counterintuitive because we're used to larger numbers being greater.
But with negatives, it's the opposite: the 'larger' negative number (in absolute value) is actually the smaller number.
So always double-check which negative number is 'higher up' the line and which is 'lower down'.

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Most popular questions from this chapter

The second side of a triangle is \(3.25 \mathrm{cm}\) longer than the first side. The third side is \(4.35 \mathrm{cm}\) longer than the second side. If the perimeter of the triangle is 26.87 \(\mathrm{cm},\) find the length of each side.

Use an inequality and the five-step process to solve each problem. An unconditional acceptance into the Master of Business Administration (MBA) program at Arkansas State University will be given to students whose GMAT score plus 200 times the undergraduate grade point average is at least \(950 .\) Chloe's GMAT score was \(500 .\) What must her grade point average be in order to be unconditionally accepted into the program?

A storekeeper goes to the bank to get \(\$ 10\) worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?

Use an inequality and the five-step process to solve each problem. Abriana rented a compact car for a business trip. At the time of the rental, she was given the option of prepaying for an entire tank of gasoline at \(\$ 3.099\) per gallon, or waiting until her return and paying \(\$ 6.34\) per gallon for enough gasoline to fill the tank. If the tank holds 14 gal, how many gallons can she use and still save money by choosing the second option?

Elsa has an average score of 82 on three tests. Her average score on the first two tests is \(85 .\) What was the score on the third test?
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