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Chapter 2: Problem 404

In the following exercises, solve each equation. $$ x+93=114 $$

Short Answer

Expert verified
x = 21

Step by step solution

01

Write down the equation

Write the given equation: \[ x + 93 = 114 \]
02

Isolate the variable

To solve for \( x \), subtract 93 from both sides of the equation: \[ x + 93 - 93 = 114 - 93 \]
03

Simplify

Simplify both sides of the equation: \[ x = 21 \]

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Key Concepts

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

Isolating the Variable
In algebra, isolating the variable is a key concept when solving equations. The goal is to get the unknown variable by itself on one side of the equation, making it easier to understand its value.
To isolate the variable, we often use inverse operations. Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division.
For example, in the equation \( x + 93 = 114 \), we must get rid of the +93 to isolate \( x \).
We do this by subtracting 93 from both sides of the equation:
\[( x + 93 ) - 93 = 114 - 93 \]
This results in \( x = 21 \), successfully isolating the variable.
Simplification
Simplification in algebra means making an expression or equation easier to work with. After isolating the variable, we simplify both sides to clearly see the solution.
Let's take another look at our equation from above:
\[x + 93 - 93 = 114 - 93 \]
Here, we notice that adding 93 and then subtracting 93 on the left side cancels each other out. This simplifies to:
\[x = 114 - 93\]
Finally, we perform the subtraction on the right side:
\[x = 21\]
  • This process is crucial as it breaks down complex expressions into simple, solvable components.
  • It ensures the steps taken are clear and logical, eliminating any extra or confusing parts from the equation.
Basic Algebra
Basic algebra involves understanding and applying fundamental operations and principles to solve equations. Let's review the principle steps we followed:
  • Understanding the equation and what is being asked
  • Isolating the variable using inverse operations
  • Simplifying both sides of the equation
In our example, we started with the equation \( x + 93 = 114 \).
The goal is to find the value of \( x \). We isolated the variable by subtracting 93 from both sides:
\[ x + 93 - 93 = 114 - 93 \]
This left us with \( x = 21 \), showing us the simple and precise steps to solve for the unknown variable. Basic algebra forms the foundation for more advanced mathematical concepts, making these steps essential for further learning.

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