Solving linear equations with variables is an essential algebra skill with countless real-world applications. The process involves using inverse operations to isolate the variable term, then determining the value that satisfies the full equation. In this post, we’ll solve the equation x + 9 = 18 + -2x for the value of x, explaining each step along the way. We’ll also explore strategies and insights on solving one-variable algebraic equations systematically.

## x + 9 = 18 + -2x What Does x Equal?

*To find the value of x in the equation x + 9 = 18 + (-2x), we can simplify it by isolating x. First, add 2x to both sides to eliminate the -2x on the right: x + 2x + 9 = 18. This simplifies to 3x + 9 = 18. Next, subtract 9 from both sides: 3x = 18 – 9, which becomes 3x = 9. Finally, divide both sides by 3 to find x: x = 9 / 3, which gives x = 3. Therefore, the solution is x = 3.*

Here’s a table to show the steps taken to solve the equation x + 9 = 18 + (-2x) and find the value of x:

Step | Equation | Simplification |
---|---|---|

Original Equation | x + 9 = 18 + (-2x) | |

Add 2x to both sides | x + 2x + 9 = 18 + (-2x) | 3x + 9 = 18 – 2x |

Subtract 9 from both sides | 3x + 9 – 9 = 18 – 2x – 9 | 3x = 9 – 2x |

Add 2x to both sides | 3x + 2x = 9 – 2x + 2x | 5x = 9 |

Divide by 5 | (3x + 2x) / 5 = 9 / 5 | x = 9 / 5 |

Final Solution | x = 9 / 5 |

So, the solution to the equation is x = 9/5 or x = 1.8.

To solve for x in the equation:

x + 9 = 18 + (-2x)

You can follow these steps to isolate x:

- Add 2x to both sides of the equation to get rid of the -2x term on the right side:

x + 2x + 9 = 18

This simplifies to:

3x + 9 = 18

- Subtract 9 from both sides of the equation to isolate the term with x:

3x = 18 – 9 3x = 9

- Finally, divide both sides by 3 to solve for x:

3x / 3 = 9 / 3 x = 3

Now, you can create a table to show the equation and the solution:

Equation | Solution |
---|---|

x + 9 = 18 + (-2x) | x = 3 |

So, the value of x that satisfies the equation is x = 3.

Reviewing Linear Equation Basics Let’s first review some key concepts about linear equations in one variable:

- They have terms with the variable x isolated on one side.
- Applying inverse operations cancels out terms containing x.
- Perform the same operations to both sides to keep equality.
- Check solutions by substituting back into the original equation.
- Many real-world formulas and models have linear equation forms.

Keeping these principles in mind, let’s solve our given equation.

Solving the Equation Step-by-Step

x + 9 = 18 + -2x

Add 2x to both sides:

x + 9 + 2x = 18 + -2x + 2x 3x + 9 = 18

Subtract 9 from both sides:

3x = 9

Divide both sides by 3:

x = 3

Therefore, x equals 3 when satisfied by the full equation.

Explanation of the Steps

- Added 2x to both sides to group and isolate x terms.
- Subtracted 9 from both sides to get x alone.
- Divided by 3, the coefficient of x, to find the value of x.
- The operations resulted in x = 3 solving the given equation.

Strategies for Solving Linear Equations

Some helpful strategies:

- Check your understanding of inverse operations to isolate variables.
- Take the process step-by-step to avoid mistakes. Don’t rush!
- Double check the solution satisfies the original equation.
- Consider how the equation models a real-world scenario.
- Build intuition by visualizing opposite operations balancing out.

Conclusion In this post, we solved the equation x + 9 = 18 + -2x for x by methodically applying inverse operations to both sides. Explaining each step reinforces good practices for equating solutions. Fluency solving one-variable linear equations provides the foundation for more complex algebraic analysis. Consistent practice builds skills essential across science, engineering, finance, and other fields relying on mathematical modeling. Each solved equation brings learners one step closer to mastery of algebraic thinking. Keep practicing solving those equations!

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