Problem 17 - Algebra 2

Question

Evaluate each expression if \(a=-5, b=6,\) and \(c=2.8\). \(|a+5|\)

Step-by-Step Solution

Answer

The evaluated expression is 0.

Step 1: Substitute the value of 'a'

The expression given is \(|a+5|\). Start by substituting \(a = -5\) into this expression. This gives us \(|-5 + 5|\).

Step 2: Simplify the inside of the absolute value

Now, simplify the expression inside the absolute value: \(-5 + 5 = 0\). So, we have \(|0|\).

Step 3: Evaluate the absolute value

The absolute value of 0 is simply 0, because absolute value represents the distance from zero on the number line, which is 0.

Key Concepts

Understanding Substitution

Substitution is a key algebra concept where we replace variables in an expression with specific values. This makes it easier for us to evaluate the expression. In our exercise, we used substitution to replace the variable 'a' with
-5. This process is useful because:

• It simplifies the analysis of an expression by using known values.
• Helps us solve equations easily by reducing abstract symbols to concrete numbers.

To substitute, we simply replace every occurrence of the variable in the expression with the given number. For example, in
\(|a + 5|\), replacing 'a' with -5 gives us \(|-5 + 5|\). This step is crucial as it sets up the simplification process.

Mastering Simplification

Simplification involves breaking down expressions into their simplest form. While abstract expressions with variables might look complicated, simplification helps to make them more manageable. After substitution, we had the expression
\(|-5 + 5|\). By simplifying within the absolute value, we performed the arithmetic operation
\-5 + 5 = 0\. Simplification has several benefits:

• It makes calculations straightforward and easy to understand.
• Reduces errors in subsequent calculations by presenting the simplest form.

After simplifying, the once complex-looking expression inside the absolute sign became zero, making the whole evaluation much simpler.

Exploring Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations. They can represent real-world problems and scenarios. Our task involved evaluating the algebraic expression
\(|a + 5|\). Here, the expression included a variable, addition operation, and an absolute value function. It's fundamental to understand:

• Variables stand for unknowns or placeholders for values, like 'a' in our expression.
• Operations like addition affect how these values interact within an expression.
• The absolute value function transforms the expression by focusing on the distance from zero.

Algebraic expressions are versatile and used widely in computes, predictions, and problem-solving scenarios. Mastering the manipulation of such expressions is essential for advancing in mathematics.