Solving Linear Equations: Solving the Equation x - 9 18 - 2x

Linear equations are a fundamental component of algebra and form the basis for many real-world applications, from budgeting to calculating distances. A linear equation in one variable is an equation that can be expressed in the form ax b c.

Understanding the Equation

Let's break down the given equation:

Given: x - 9 18 - 2x

Our goal is to solve for x. This involves manipulating the equation to isolate x on one side of the equation.

Step-by-Step Solution

Let's walk through the solution step by step:

Step 1: Combine like terms. To do this, we need to move all terms with x to one side and constants to the other. Step 2: Add 2x to both sides of the equation to get rid of the -2x on the right side and combine like terms on the left side. Step 3: Simplify the left side of the equation. Step 4: Simplify the right side of the equation. Combine -9 and 18 to get 9. Step 5: Divide both sides by 3 to isolate x.

Performing the Operations

Let's perform these steps:

Add 2x to both sides: x - 9 2x 18 - 2x 2x Simplify the left side: 3x - 9 18 Add 9 to both sides to isolate the term with x: 3x - 9 9 18 9 Perform the addition: 3x 27 Divide both sides by 3: ( frac{3x}{3} frac{27}{3} ) Final result: x 9

Verification

Let's verify the solution by substituting x 9 back into the original equation:

Original equation: x - 9 18 - 2x Substitute x 9: 9 - 9 18 - 2(9) Simplify both sides: 0 18 - 18 Final check: 0 0

The left and right sides are equal, confirming that our solution is correct.

Conclusion: The solution to the equation (x - 9 18 - 2x) is (x 9).

Frequently Asked Questions:

Q1: What is a linear equation?

A linear equation is an equation that can be expressed in the form ax b c, where a, b, and c are constants and x is the variable. Linear equations are fundamental to algebra and are used in many real-world applications.

Q2: How do I solve a linear equation?

To solve a linear equation, you need to isolate the variable on one side of the equation. This typically involves performing the same operations on both sides to simplify the equation step by step.

Q3: Why is it important to check the solution?

Checking the solution is important because it ensures the answer is accurate. Substituting the solution back into the original equation helps verify that the solution satisfies the equation.