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Chapter 2: Problem 1

Solve for \(x: x-c=d\).

Short Answer

Expert verified
The solution for \(x\) is \(x = d + c\).

Step by step solution

01

Understand the equation

We begin with the equation given: \(x - c = d\). Our goal is to solve for \(x\), which means we need to isolate \(x\) on one side of the equation.
02

Add \(c\) to both sides

To isolate \(x\), we add \(c\) to both sides of the equation. The equation becomes \(x - c + c = d + c\).
03

Simplify the equation

On the left side of the equation, \(-c + c\) cancels out, leaving us with \(x\). The equation simplifies to \(x = d + c\).

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Key Concepts

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

Solving Equations
Solving equations involves finding the value of the unknown variable that makes the mathematical statement true. These equations guide us to figure out how variables relate to each other. To solve the equation \(x - c = d\), we start by understanding the structure of the equation.
  • It's essential to identify what we are solving for, which in this case, is \(x\).
  • We aim to find the value of \(x\) that satisfies the equation.
  • This requires manipulating the equation according to algebraic rules to find \(x\).
Approaching the equation methodically ensures we correctly find the answer and develop a systematic way to tackle similar problems.
Isolation of Variable
The isolation of a variable is a critical step in solving equations. It's all about getting the variable, in this instance \(x\), by itself on one side of the equation. Here鈥檚 how you can think about it:
  • The equation \(x - c = d\) suggests that \(c\) is subtracted from \(x\).
  • To isolate \(x\), we undo this subtraction.
Adding \(c\) to both sides of the equation helps us remove \(c\) from the left side, achieving our goal of having \(x\) alone. This means that whatever you do to one side of the equation, you must do to the other to maintain balance.
This balance is the cornerstone of algebraic manipulation and ensures that the equality holds true throughout the solving process.
Inverse Operations
Inverse operations are key to solving equations and play a major role in successfully isolating variables. Simply put, they are operations that "undo" each other. When you think of solving \(x - c = d\), here鈥檚 how inverse operations come into play:
  • Subtraction and addition are inverse operations.
  • To remove \(-c\), you perform the inverse operation, which is to add \(c\).
This use of inverse operations not only simplifies the equation to \(x = d + c\), but also serves as a reliable method to solving various types of equations.
Using inverse operations helps keep the equation balanced while progressing towards the solution, making it an essential skill in algebra.

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