Problem 82 In Exercises $73-84$, evaluate... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 82

In Exercises $73-84$, evaluate the given expression. $$|7-10|-(7-10)$$

Short Answer

Expert verified

The value of the expression is 6.

Step by step solution

Evaluate the Absolute Value Expression

The given expression is $|7 - 10| - (7 - 10)$. First, evaluate the absolute value part: $|7 - 10| = | -3| = 3$

Evaluate the Subtraction Expression

Now, evaluate the subtraction part inside the parentheses: $7 - 10 = -3$

Substitute the Values Back

Substitute the values from Step 1 and Step 2 back into the original expression: $3 - (-3)$

Simplify the Expression

Simplify the expression from Step 3. Remember that subtracting a negative number is the same as adding its positive: $3 - (-3) = 3 + 3 = 6$. Thus, the final value is 6.

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Key Concepts

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

Absolute Value

Absolute value is an important concept in algebra, often represented by two vertical lines around a number or expression (e.g., $|x|$). The absolute value of a number refers to its distance from zero on the number line, regardless of direction. This means the absolute value is always a non-negative number.

In our exercise, we encounter $|7-10|$. Since $7-10$ evaluates to $-3$, its absolute value is $|-3|=3$. Notice how we ignore the negative sign. Absolute value essentially strips away the direction, focusing solely on the magnitude.

Subtraction

Subtraction is one of the fundamental operations in arithmetic and algebra. It involves finding the difference between two numbers. The symbol for subtraction is $-$. In our exercise, we see $7-10$. Here, we subtract 10 from 7, which gives us $-3$.

When dealing with subtraction, it's essential to understand that the operation signifies taking away one quantity from another. Importantly, subtracting a larger number from a smaller one results in a negative value, as seen in our example where $7-10$ equals $-3$.

Simplification

Simplification involves making an expression easier to work with by reducing it to its simplest form. The goal is to make calculations straightforward and error-free. For our given expression $|7-10| - (7-10)$, we first evaluated each part and then combined them.

Step-by-step, we:
1. Found the absolute value: $|7-10| = 3|$.
2. Calculated the subtraction: $(7-10) = -3$.
3. Combined the results into the original expression: $3 - (-3)$.
Finally, we simplified this to $3 + 3 = 6$.

Remember, when simplifying, pay attention to mathematic rules like subtracting a negative (which turns into addition) and combining like terms.

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91影视

In Exercises \(73-84\), evaluate the given expression. $$|7-10|-(7-10)$$

Short Answer

Step by step solution

Evaluate the Absolute Value Expression

Evaluate the Subtraction Expression

Substitute the Values Back

Simplify the Expression

Key Concepts

Absolute Value

Subtraction

Simplification

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