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Chapter 1: Problem 68

A number minus three equals 1 .

Short Answer

Expert verified
The number is 4.

Step by step solution

01

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: \[ x - 3 = 1 \]
02

Isolate the variable

To find the value of the number, add 3 to both sides of the equation to isolate the variable. \[ x - 3 + 3 = 1 + 3 \]
03

Simplify the equation

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Find the average of each group of numbers. -15,29,8,-6

Use the distributive property to rewrite each expression. $$ -\frac{1}{4}(8 x+3) $$

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 3 if the sum of its digits is divisible by \(3,\) and not otherwise. (a) Is 4,799,232 divisible by \(3 ?\) (b) Is 2,443,871 divisible by \(3 ?\)

Twice the product of -1 and \(6,\) subtracted from -4

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. Work Exercises 139-142 in order, to find the average of \(23,18,13,-4,\) and -8 Find the sum of the given group of numbers.
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