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Chapter 2: Problem 73

The number \(-6\) is 2 more than an unknown number. Find the unknown number.

Short Answer

Expert verified
The unknown number is -8.

Step by step solution

01

Understand the Problem

The problem states that \(-6\) is 2 more than an unknown number. We need to find out what this unknown number is.
02

Set Up the Equation

Let the unknown number be represented by \(x\). According to the problem, \(-6 = x + 2\). We will use this equation to find \(x\).
03

Isolate the unknown variable

To solve for \(x\), subtract 2 from both sides of the equation: \(-6 - 2 = x + 2 - 2\). This simplifies to \(-8 = x\).
04

Solve the Equation

Now, we have the simple equation \(x = -8\), which gives us the value of the unknown number.

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Key Concepts

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

Understanding the Unknown Variable
In algebra, an "unknown variable" represents a value we need to discover. It's usually symbolized by a letter like \( x \), \( y \), or \( z \). This concept is fundamental in forming equations to solve real-world problems. In our exercise, the unknown number is what makes \(-6\) exactly 2 more than it.To grasp the unknown variable:
  • Think of it as a placeholder for a specific number you haven't identified yet.
  • You create an equation where this unknown appears, helping you explore the relationships between known and unknown quantities.
Familiarity with unknown variables strengthens your ability to tackle various algebraic expressions and solve different types of problems efficiently.
Solving Equations Step-by-Step
Solving equations is a methodical process where we determine the value of the unknown variable. Each step in the process inches closer to the solution.Here's how you solve the equation presented in the exercise:
  • Step 1: Start with understanding the problem. Recognize that the number \(-6\) is 2 more than an unknown \(x\).
  • Step 2: Set up the equation based on the problem: \(-6 = x + 2\).
  • Step 3: Isolate the unknown variable. To do this, you perform operations that keep the equation balanced. Subtract 2 from both sides: \(-6 - 2 = x + 2 - 2\).
  • Step 4: Simplify the equation to find \(x = -8\).
These steps exemplify the straightforward logic used in solving equations. Remember, balance is key鈥攚hatever you do on one side of the equation, do the same on the other to maintain equality.
Characteristics of Linear Equations
Linear equations are a vital type of algebraic equations. They are characterized by their straightforward format, where each term is either a constant or the product of a constant and a variable.For our exercise, the equation \(-6 = x + 2\) is identified as a linear equation because:
  • The highest power of the variable (\(x\)) is one, representing a straight line if graphed.
  • It's a simple equation involving only addition or subtraction operations.
  • It has two terms that relate a constant and an unknown variable.
Linear equations often model simple relationships between variables, making them an essential tool in problem-solving and understanding algebraic principles.

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Most popular questions from this chapter

The number \(-5\) is 8 more than an unknown number. Find the unknown number.

Simplify the given expression. \(\frac{10-7-(-11)}{-3}\)

Two less than eight times an unknown number is \(-74\). Find the unknown number.

Three more than eight times an unknown number is \(-29\). Find the unknown number.

Solve the given equation for \(x\). \(x+2=1\)
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