Problem 89 - Algebra 1

Question

Evaluate the expression for the given value of the variable. $$5 x^{2} \text { when } x=0.3$$

Step-by-Step Solution

Answer

The evaluated result of the expression is 0.45

Step 1 - Identify the given expression and the variable

The given expression is \(5x^2\) and the variable \(x\) is given as 0.3

Step 2 - Substitute the given value into the expression

We will replace \(x\) in the expression with 0.3. So it will become \(5 * (0.3)^2\)

Step 3 - Evaluate the expression

Now, we have to compute the expression \(5 * (0.3)^2\). First calculate the square of 0.3, which equals 0.09, and then multiply by 5, yielding 0.45

Key Concepts

Substitution

Substitution is an essential skill when handling algebraic expressions. It involves replacing a variable in an expression with a given value. Picture simplifying a recipe where you substitute an ingredient for another based on what's available in your pantry. This concept works similarly in algebra.

For example, in the expression \(5x^2\), "\(x\)" is our variable. By substituting, we replace "\(x\)" with the actual number value provided. In our problem statement, we have \(x = 0.3\). When we substitute, the expression becomes \(5 \cdot (0.3)^2\).

To substitute correctly, always ensure you've placed the value into every occurrence of the variable. Doing so maintains the mathematical integrity of the equation. This is the first step toward solving or simplifying any complex algebraic expression.

Squaring Numbers

Squaring numbers is one of the fundamental operations in mathematics and it is vital to know how it affects variables in equations. "Squaring" simply means multiplying a number by itself.

In our example, the core task was to compute \( (0.3)^2 \). Here, "0.3" is multiplied by "0.3", providing a product of 0.09.

Squaring can affect the value significantly as the result is always non-negative (positive or zero), regardless if the number itself is negative or positive. Understanding this helps particularly when dealing with quadratic expressions or equations. Remember to always complete the squaring step before any additional operations, like multiplication by a coefficient, to ensure accuracy.

Variable Evaluation

Variable evaluation is the last step in solving a substituted equation. It's the process of calculating the actual number result from the expression after substitution and computation.

Once substitution and squaring are done, you directly evaluate the expression. For example, after squaring 0.3 to get 0.09, the expression \(5 \cdot 0.09\) remains. Here, we multiply 0.09 by 5 to reach the final answer of 0.45.

Evaluating helps determine the exact numerical value the algebraic expression represents for the given variable value. This step is crucial for obtaining accurate answers and is often used to solve equations, making it crucial for students tackling any math-related problems. Always ensure each mathematical order of operations—brackets, exponents, multiplication, division, addition, subtraction—is followed correctly for precise results.