Problem 5 - Precalculus

Question

Evaluate each expression. $$|-1+3|$$

Step-by-Step Solution

Answer

The evaluated expression is 2.

Step 1: Identify Terms Inside Absolute Value

Identify the expression inside the absolute value symbols. In this case, the expression is \(-1 + 3\).

Step 2: Calculate Expression Inside Absolute Value

Calculate the expression that is inside the absolute value. This is done by adding \(-1\) and \(3\): \(-1 + 3 = 2\).

Step 3: Apply Absolute Value Function

The absolute value function turns any number into its non-negative equivalent.Apply the absolute value function to \(2\): \(|2| = 2\).

Key Concepts

Evaluating Expressions

Understanding how to evaluate expressions is essential because it lays the groundwork for more complex mathematical ideas. Begin by recognizing parts within the expression. For our example, the expression to evaluate is inside absolute value brackets: \(|-1 + 3|\).
Expressions like these involve performing operations first before applying additional conditions such as absolute values.
This is common in mathematical problems where you often encounter expressions within a broader problem.

• First, focus on the expression inside, ignoring the absolute value brackets for a moment.
• Then, solve the expression in a straightforward manner.

Once the expression is simplified internally, any further rules, like taking the absolute value, are applied.
There's a reason why evaluating expressions step-by-step is important—it ensures accuracy and builds proper understanding aligned with mathematical principles.

Step-by-Step Solution

Breaking down a problem into smaller steps is commonly known as a 'step-by-step solution'. This approach aids in conquering even the trickiest problems by making them less daunting.
For instance, solving the expression \(|-1 + 3|\), involves a systematic approach:

• **Step 1:** Identify the terms inside the absolute value. Here, it's \(-1 + 3\).
• **Step 2:** Perform the arithmetic operations present. Compute the expression within the absolute value: \(-1 + 3 = 2\).
• **Step 3:** Apply the absolute value to the result from the previous step. In this case, \(|2| = 2\).

Step-by-step problem solving promotes clarity and enhances understanding by segregating tasks and addressing them in sequence.
This method helps prevent errors and equips you with strategies for tackling more complex equations with confidence.

Mathematical Operations

Mathematical operations are the fundamental actions we perform on numbers and expressions. These include addition, subtraction, multiplication, and division.
In our example of evaluating \(|-1 + 3|\), the operation involved is addition, where we add the values -1 and 3.
Understanding these operations is crucial because every more advanced mathematical topic builds upon these foundations.

• Addition, as seen, brings together numbers to find their collective sum.
• Subtraction removes a quantity from another to find a difference.
• Multiplication scales a number by another.
• Division breaks a number into smaller parts.

Once basic operations are second nature, you can apply them to various contexts, such as evaluating expressions, solving equations, or simplifying algebraic fractions.
Practicing these operations solidifies your mathematical skills and enhances your problem-solving abilities.