Problem 137 Fill in the blank with \(<,=\... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 1: Problem 137

Fill in the blank with $<,=$ or $\rangle$. $-10$ _____ $-|-2|$

Short Answer

Expert verified

$-10 < -|-2|$ because $-10 < -2$.

Step by step solution

Simplify Absolute Expression

First, let's simplify the expression on the right side, which is $-|-2|$. The absolute value of $-2$ is $|-2| = 2$. Thus, $-|-2|$ simplifies to $-2$.

Compare Two Values

Now we need to compare $-10$ and $-2$. Since $-10$ is more negative than $-2$, it follows that $-10 < -2$.

Fill in the Blank

Based on the comparison, we conclude that the inequality symbol to fill in the blank is $<$. Thus, the completed expression is $-10 < -|-2|$.

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Key Concepts

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

Understanding Absolute Value

Absolute value is a mathematical function that tells us the distance of a number from zero on a number line. It is represented by two vertical bars. For instance, the absolute value of -2 is written as $|-2|$, which equals 2. The absolute value always converts any number to a positive value or zero because distance cannot be negative.
In our exercise, we first find the absolute value of -2, turning it into 2, before proceeding with any additional computations. This step ensures that we deal with numbers it represents on a purely positive scale, making further problem-solving more straightforward.

Dealing with Negative Numbers

Negative numbers are numbers less than zero. They have a "-" sign in front of them and are located to the left of zero on a number line. When comparing negative numbers, it is essential to understand that the number with the "larger" absolute value is actually smaller.
For instance, -10 is more negative than -2 because 10 is greater than 2, thus -10 is less than -2 when placed on a number line.
Understanding this concept aids in accurately comparing and writing inequalities between negative numbers, as shown where -10 is less than -2 $ (-10 < -2) $.

Simplifying Expressions

Simplifying expressions involves making them easier to understand or compute. The exercise required us to simplify the expression -|-2|, which involves handling the absolute value first.
After the absolute value turns -2 into 2, we then apply the negative sign outside the absolute value to attain -2 again. Simplifying helps us compare numbers accurately, especially when they involve absolute values or negative signs.

First, tackle absolute value operations.
Apply any signs outside of these absolute value results.
Perform any needed comparisons or operations afterward.

This process can clarify even seemingly complex expressions, ensuring a correct comparison or calculation in steps like the one carried out in our exercise.

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91影视

Fill in the blank with \(<,=\) or \(\rangle\). \(-10\) _____ \(-|-2|\)

Short Answer

Step by step solution

Simplify Absolute Expression

Compare Two Values

Fill in the Blank

Key Concepts

Understanding Absolute Value

Dealing with Negative Numbers

Simplifying Expressions

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