Problem 54 - Elementary Algebra

Question

Determine each of the values, \(|-2|+|-9|\)

Step-by-Step Solution

Answer

Answer: The value of the expression |-2| + |-9| is 11.

Step 1: Calculate the absolute values of the numbers

In order to do this, we will apply the absolute value function to each number: \(|-2| = 2\) and \(|-9| = 9\)

Step 2: Add the absolute values

Now that we have the absolute values, we can add them together: \(2 + 9 = 11\) Thus, the value of the given expression \(|-2| + |-9|\) is \(11\).

Key Concepts

Addition of Numbers

Addition is a basic mathematical operation that combines two or more values to get a total sum. Understanding addition is essential for tackling more complex math problems. In addition, - You simply combine the given numbers. - The order does not affect the result (this is called the commutative property).
Let's consider adding two numbers a and b, which is expressed as:\[a + b = c\]where \(c\) is the result of the addition. When you're adding numbers, it's like collecting objects together, for instance:

• Finding the total of the items.
• Balancing a checkbook by adding deposits.
• Ensuring you have all the ingredients for a recipe by tallying each measurement.

This simple operation forms the basis for understanding more complicated algebraic expressions and other advanced topics in mathematics. Remember, practice makes perfect!

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. They are essential in algebra because they help express mathematical statements.
An algebraic expression can take various forms. For example, \(5x + 3\) is an algebraic expression containing a variable \(x\), a coefficient \(5\), and a constant term \(3\). Here, the addition sign ties together the terms, showing how expressions can be composed of different parts.
To solve an algebraic expression, you might need to perform different operations, such as addition or subtraction, and apply rules of algebra. Some practical instances of using algebraic expressions are:

• Calculating the area of shapes.
• Solving everyday problems, like finding the price of items based on quantities.
• Financial planning and budgeting.

Understanding how to interpret and manipulate these expressions is foundational for success in algebra.

Mathematical Operations

Mathematical operations, like addition, subtraction, multiplication, and division, are actions you perform on numbers or expressions to find results. These operations are the building blocks for tackling any math problem.
Each operation serves a specific purpose:

• Addition: Combining numbers to find their total.
• Subtraction: Finding the difference between numbers.
• Multiplication: Scaling one number by another.
• Division: Splitting numbers into equal parts.

Knowing when and how to use these operations is key to solving both simple and complex problems. For instance, solving a problem like \(|-2| + |-9|\)requires calculating absolute values first, then applying addition. Precision and understanding the rules of operations can help tremendously in progressing through math challenges effectively. This skill serves not only in academia but in daily life situations such as cooking or financial management.