Problem 9 - Algebra 2 and Trigonometry

Question

Find the value of each given expression. \(|4-6+(-2)|\)

Step-by-Step Solution

Answer

The value is 4.

Step 1: Simplify Inside the Parentheses

Start by calculating the expression inside the absolute value symbol, \[ 4 - 6 + (-2) \]First, simplify the subtraction:\[ 4 - 6 = -2 \]Then, add \(-2\):\[ -2 + (-2) = -4 \]

Step 2: Apply Absolute Value

Now, apply the absolute value to the result from Step 1: \[ |-4| \]The absolute value of a number is its distance from zero on the number line, which is always a non-negative number. Therefore,\[ |-4| = 4 \]

Key Concepts

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form. This makes calculations easier and more manageable. In the given expression, \(4 - 6 + (-2)\), simplifying involves performing operations step by step within any grouping symbols, like parentheses if they're present.
Here's how you simplify:

• Evaluate any operations inside parentheses or other grouping symbols first.
• Follow the order of operations, sometimes remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

For our expression, start simplification by working from left to right, considering subtraction and addition operations. Break down the expression in stages to ensure clarity and accuracy.
By simplifying, we can convert complex mathematical phrases into simpler numbers, making equations easier to understand and solve.

Subtraction

Subtraction is the process of taking one number away from another, represented by the "-" symbol. It is one of the basic arithmetic operations and is fundamental to understanding math. In the context of the expression \(4 - 6\), subtraction will give us a negative result since 6 is larger than 4.
When subtracting:

• Identify which number is being subtracted from which (the minuend and the subtrahend).
• Perform the subtraction: \(4 - 6 = -2\).

Subtraction can also be viewed as the addition of a negative, which can be useful. For example, when solving \(4 - 6 + (-2)\), you can think of it as adding the negative value of 6 and then adding another negative 2, effectively combining these values to reach the answer.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. It is represented by the "+" symbol. In the given mathematical expression \(-2 + (-2)\), addition is used to combine negative numbers.
Here are some tips for understanding addition:

• Addition can be straightforward when dealing with positive numbers, but often involves considering sign when negatives are involved.
• When adding negative numbers, you're essentially moving further left on the number line.
• With \(-2 + (-2) = -4\), realize that adding two negative numbers increases the magnitude of negativity.

Addition helps us build much larger numbers by combining smaller values or, as in this case, helping to simplify expressions as part of a problem-solving approach.