Problem 113 - Introductory Algebra for College Students

Question

Will help you prepare for the material covered in the next section. Solve: \(\quad 4=0.25 B.\)

Step-by-Step Solution

Answer

The value of B is 16.

Step 1: Identify the Equation

The given equation is \(4 = 0.25B\). Here, we need to solve for \(B\).

Step 2: Isolate the Variable

To isolate \(B\), divide both sides of the equation by \(0.25\). That is, \(B = \frac{4}{0.25}\).

Step 3: Calculate the Value

Calculating the right side, \(B = 16\).

Key Concepts

Algebraic Equations

An algebraic equation is a mathematical statement that shows the equality of two expressions, which are typically connected by the equals sign (=). The simplest form of an algebraic equation is a linear equation, which is an equation of the first degree, meaning it contains no exponents greater than one. An example would be the equation presented in the exercise, where we have to solve for a variable, represented by the letter 'B'.

Algebraic equations are the foundation of algebra and are used to model a wide range of real-world situations. When solving an algebraic equation, the goal is to determine the value of the unknown variable that makes the equation true. In doing so, one applies basic mathematical operations to both sides of the equation in a strategic way to isolate the variable and find its value.

Isolate the Variable

One of the essential strategies in algebra is to isolate the variable. This process means to manipulate the equation in such a way that the variable you are solving for ends up alone on one side of the equation. The objective is to have the variable by itself and everything else on the opposite side.

To achieve this, one must understand the idea of balance. An equation is like a scale; whatever you do to one side must also be done to the other to maintain equality. In the given exercise, the process of isolating the variable, 'B', involves dividing both sides of the equation by 0.25, which is the coefficient of 'B'. Isolating the variable allows us to solve for it effectively and is a crucial step in solving algebraic equations.

Mathematical Operations

Mathematical operations are procedures that are performed on numbers and variables. The four basic mathematical operations are addition, subtraction, multiplication, and division. In the context of algebra, these operations are used to transform equations into a solvable form.

When solving equations, it's important to perform operations with precision and to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the given exercise, division is the key operation used to isolate 'B'. Here, it's crucial to understand that dividing both sides of the equation by the same non-zero number does not change the equality, thus helping with the isolation of the variable to find its value.