Problem 42 - Algebra 1

Question

Evaluate the expression for the given value of the variable. (Review 1.3 and 2.5 for 4.2 ) \(3 x+9\) when \(x=2\)

Step-by-Step Solution

Answer

The evaluated result of the expression \(3x + 9\) where \(x = 2\) is \(15\).

Step 1: Substitute the given value for \(x\) into the expression

We replace \(x\) in the expression \(3x + 9\) with the given value, which is \(2\). This gives us: \(3(2) + 9\)

Step 2: Multiply

Perform the multiplication first, as per the BODMAS rule (Bracket, Orders, Division and Multiplication, Addition and Subtraction). So, \(3 \times 2\) becomes \(6\). Hence the expression now will be \(6 + 9\)

Step 3: Add

Next, we perform addition of the numbers which means adding \(6 + 9\). This results in a final value of \(15\).

Key Concepts

Substitution

Substitution is one of the foundational techniques in algebra and mathematics. It involves replacing a variable in an algebraic expression with a specific value. This helps us change an expression into something concrete that we can calculate easily.
For example, in the expression \(3x + 9\), we are initially working with an unknown variable, \(x\). However, when we're given that \(x = 2\), we can substitute \(2\) directly into the expression in place of \(x\). The expression becomes \(3(2) + 9\), which is now easier to handle because all components are numbers.

• The first step is always identifying the variable to be replaced.
• The second step is to insert the given value wherever the variable appears in the expression.

Once the substitution is made, the expression is ready for further calculations, guiding us closer to a final numerical result.

BODMAS Rule

The BODMAS rule is a critical principle to understand when evaluating mathematical expressions. BODMAS stands for:

• Brackets
• Orders (such as powers and roots)
• Division
• Multiplication
• Addition
• Subtraction

This rule dictates the order in which operations should be performed to ensure accurate results. In our expression, after substitution, we have \(3(2) + 9\). According to the BODMAS rule, multiplication should come before addition.
So, even if addition ("+ 9") seems tempting to perform first, BODMAS reminds us that we need to multiply \(3 \times 2\) resulting in \(6\), before proceeding to any additions.
Understanding and applying BODMAS helps prevent misconceptions and errors when faced with complex expressions.

Basic Algebra

Basic algebra involves manipulating mathematical expressions and solving for unknowns. The key processes include substitution, using operations like addition, subtraction, multiplication, and division, and applying rules like BODMAS.
In our case, the expression \(3x + 9\) becomes manageable through a sequence of steps. After substitution and adhering to the BODMAS rule by resolving multiplication before addition, we find \(3(2) + 9\) simplifies Step by step, it turns into \(6 + 9\), finally reaching the answer \(15\).
Algebra helps in forming a bridge between arithmetic and the more advanced mathematics. Mastering it enables students to tackle a wide range of mathematical problems with confidence. Each solved problem builds intuition for the structure and logic underpinning math.