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Chapter 2: Problem 84

The number \(-6\) is 8 more than an unknown number. Find the unknown number.

Short Answer

Expert verified
The unknown number is -14.

Step by step solution

01

Set up the equation

We are given that the number \(-6\) is 8 more than an unknown number, let's denote the unknown number as \(x\). Based on the description, we set up the equation: \(-6 = x + 8\).
02

Solve for the unknown number

To find the value of \(x\), we need to isolate \(x\) on one side of the equation. To do this, subtract 8 from both sides of the equation:\[-6 - 8 = x + 8 - 8\]This simplifies to:\[-14 = x\].

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Key Concepts

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

Equation Solving
Equation solving is the process of finding the value of unknown quantities or variables in mathematical statements. When we talk about equations, we refer to expressions set equal to each other.
In our exercise, the equation is given as \[-6 = x + 8\].
The equal sign indicates that both sides of the equation have the same value. Steps involved in equation solving typically include:
  • Identifying the equation based on a problem situation.
  • Replacing unknowns with variables such as \(x\), \(y\), etc.
  • Using mathematical operations to manipulate the equation for finding unknowns.
The key is keeping the equation balanced: whatever you do to one side, you must do to the other side, maintaining equality.
Unknown Number
Finding an unknown number involves determining the value of a quantity that isn't specified in the problem. In our example, the unknown number is represented by the variable \(x\).
Using variables allows us to work with equations without knowing the actual value immediately.
The problem states that \[-6\]is \[8\]more than an unknown number. So, we set this unknown as \(x\) and express it as \[x + 8\].
This way of thinking transforms complex word problems into simple equations, where our goal is to solve for the unknown.
Isolate Variable
Isolating a variable means rearranging an equation so that the variable is by itself on one side. This is the key step to finding the value of an unknown number.
To isolate \(x\), you must perform operations that reverse those affecting it. In our exercise, we needed to remove \[+8\]from \[x + 8\].
We did this by subtracting \[8\] from both sides: \[-6 - 8 = x + 8 - 8\]. After simplifying, it becomes \[-14 = x\].
This process of performing inverse operations helps "unlock" the solution, revealing the value of \(x\).
  • Keep the equation balanced by performing the same operation on both sides.
  • Use inverse operations: addition's inverse is subtraction, and multiplication's inverse is division.
Understanding these concepts makes isolating variables easy and logical.

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