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Chapter 2: Problem 2

For exercises 1-10, solve. $$ x+6=30 $$

Short Answer

Expert verified
x = 24

Step by step solution

01

- Identify the Equation

The given equation is: x + 6 = 30
02

- Isolate the Variable

To isolate the variable x, subtract 6 from both sides of the equation. x + 6 - 6 = 30 - 6
03

- Simplify

Simplify both sides of the equation to solve for x. x = 24

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Key Concepts

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

Isolating the Variable
One of the first steps in solving a linear equation is isolating the variable. This means you want to get the variable by itself on one side of the equation. In our example, the equation is: \[ x + 6 = 30 \]. Here, the goal is to isolate \(x\).
By isolating the variable, you simplify the equation to make it easier to see the value of the unknown.
The primary technique for isolating \(x\) is to reverse the operations being performed on it:
  • If something is added to the variable, subtract it from both sides of the equation.
  • If something is subtracted from the variable, add it to both sides of the equation.
In our example, since we have \(x + 6\), we subtract 6 from both sides to isolate \(x\): \[ x = 30 - 6 \].
Simplifying this, we see that \(x = 24\).
Always remember: the main goal is to get the unknown variable alone on one side.
Addition and Subtraction in Equations
When working with equations in elementary algebra, addition and subtraction are fundamental operations. They help us move terms from one side of the equation to the other.
Let's break down the example: \[ x + 6 = 30 \]. Step-by-step, we need to subtract 6 from both sides:
  • First, write down the equation: \( x + 6 = 30 \).
  • Then, subtract 6 from both sides: \( x + 6 - 6 = 30 - 6 \).
  • The subtraction cancels the +6 on the left side, leaving \(x\) alone: \( x = 24 \).
This step removes any additional numbers attached to the variable, making it easier to see the solution.
It's important to perform the same operation on both sides of the equation to keep it balanced.
Elementary Algebra
At its core, elementary algebra involves solving for unknowns using basic mathematical operations. For our example problem, we started with: \[ x + 6 = 30 \].
The process of solving this follows these key principles:
  • Identify the equation and the variable you need to solve for.
  • Use addition or subtraction to move numbers from one side of the equation to the other.
  • Isolate the variable by undoing the addition or subtraction.
Therefore, we subtracted 6 from both sides to isolate \(x\): \( x = 24 \).
Elementary algebra sets the foundation for more advanced topics in mathematics. Mastering basic operations and understanding how to manipulate equations are crucial skills that will be valuable in more complex problems.
With practice, you will develop stronger skills in isolating variables and using addition and subtraction in more challenging equations.

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Most popular questions from this chapter

Find the enrollment at Oregon State University before the increase. Round to the nearest whole number. Oregon State University saw the biggest growth, a \(5.3\) percent jump of 1,302 students. Portland State University grew by only \(1.5\) percent, but remains the state's largest university with 28,958 students. (Source: www.oregonlive .com, Nov. 10. 2011)

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