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Chapter 2: Problem 99

In Exercises 97-102, evaluate the expression. $$ -12-2+|-3| $$

Short Answer

Expert verified
-11

Step by step solution

01

Find the Absolute Value of -3

The absolute value of a number is its distance from zero on a number line, ignoring whether it is to the left or right of zero. For \(-3\), the absolute value is \(3\), because if you walk \(3\) steps from \(0\) on a number line, you will be at \(-3\). So, \(-12-2+|-3|\) becomes \(-12-2+3\).
02

Perform the Subtraction and Addition Operations in Left-to-Right Order

Subtract \(2\) from \(-12\) to get \(-14\). Then, add \(3\) to \(-14\) to get \(-11\). So, the expression \(-12-2+3\) simplifies to \(-11\).
03

Final Answer

The final answer is \(-11\).

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Key Concepts

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

Expressions Evaluation
Evaluating mathematical expressions involves finding the value of an expression by following a set of established rules. This task can seem complex, especially when expressions include different operations and terms.
  • Absolute values, such as \(|-3|\), require you to determine the positive distance of a number from zero on the number line, effectively considering only the magnitude and not the sign of the number.
  • The expression \(-12 - 2 + |-3|\) requires simplifying step-by-step, starting by evaluating the absolute value of \(-3\).
Applying this understanding, you switch out \(|-3|\) with \(+3\), giving us the modified expression \(-12 - 2 + 3\). The goal is to simplify from this point on.
Order of Operations
Understanding the order of operations is crucial in correctly simplifying any mathematical expression. Following these rules ensures an accurate result.
  • Always start with operations inside parentheses. While there are no traditional parentheses in the expression \(-12-2+|-3|\), the absolute value brackets function similarly.
  • Proceed with any other operations such as exponents, multiplication, division, addition, and subtraction, in a specific sequence: parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).
For the expression \(-12 - 2 + 3\), handle subtraction and addition from left to right. Perform subtraction to find \(-14\) and then add \(+3\) to find the final value - \(-11\).
Negative Numbers
Negative numbers often appear in mathematical expressions and can sometimes make expressions seem more complicated than they actually are. It's important to understand how they interact in operations such as addition and subtraction.
  • Negative numbers are those less than zero, and they appear to the left on a number line.
  • When subtracting a number, think of it as adding a negative number. Conversely, adding a negative number effectively means you are subtracting its positive counterpart.
In the expression \(-12 - 2 + 3\), the interaction of these negative numbers is key. Subtracting \(-2\) means moving further left on the number line, leading to \(-14\), whereas adding \(+3\) shifts the result to the right, arriving at \(-11\).

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Most popular questions from this chapter

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