Problem 68 - Beginning and Intermediate Algebra

Question

A number minus three equals 1 .

Step-by-Step Solution

Answer

The number is 4.

Step 1: Identify the equation

Start by writing down the equation from the problem statement. The problem says 'A number minus three equals 1'. This can be written as: \[ x - 3 = 1 \]

Step 2: Isolate the variable

To find the value of the number, add 3 to both sides of the equation to isolate the variable. \[ x - 3 + 3 = 1 + 3 \]

Step 3: Simplify the equation

Now, simplify both sides of the equation: \[ x = 4 \]

Key Concepts

Basic Algebra

Basic algebra is the foundation of higher-level math and involves working with symbols (often letters) to represent numbers in equations and expressions. Understanding algebra is crucial because it helps you work with abstract concepts and forms the basis for solving all kinds of mathematical problems. In the given exercise, we start with the equation:

\[ x - 3 = 1 \].

Here, \( x \) is a variable representing an unknown number. Using algebra, we aim to find the value of this unknown.

Variable Isolation

Variable isolation is the process of manipulating an equation to get the variable by itself on one side of the equation. This technique allows us to determine the value of the unknown quantity.

In our example, the equation is \[ x - 3 = 1 \], and our goal is to isolate \( x \). To do this, we need to get rid of the number subtracted from \( x \).

We add 3 to both sides of the equation:
\[ x - 3 + 3 = 1 + 3 \].

Adding 3 cancels out the -3 on the left side of the equation, helping us to isolate \( x \).

Simplifying Equations

Simplifying equations is a crucial step in solving algebraic equations. Once we have isolated the variable by performing the same operations on both sides, we proceed to simplify the equation.

In our example, after adding 3 to both sides, the equation becomes: \[ x = 4 \].

Simplifying means combining like terms or reducing the equation to its simplest form. This step confirms the final value of the variable. Here, we see that \( x = 4 \) is the solution. The unknown number originally subtracted by 3 to equal 1 is indeed 4. This process shows how algebra helps us accurately pinpoint the value of unknowns.