Select The Statement That Is True For Solving The Equation $x-6=18$.A. Add 6 To Both Sides Of The Equal Sign. $x=24$.B. Subtract 6 From Both Sides Of The Equal Sign. \$x=24$[/tex\].C. Add 6 To Both Sides Of The Equal

by ADMIN 222 views

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, $x-6=18$, and explore the correct method to isolate the variable xx. We will examine three possible statements and determine which one is true.

Understanding the Equation

The given equation is $x-6=18$. Our goal is to isolate the variable xx and find its value. To do this, we need to get rid of the constant term, −6-6, that is being subtracted from xx.

Analyzing the Options

Let's examine the three possible statements:

A. Add 6 to both sides of the equal sign. $x=24$

B. Subtract 6 from both sides of the equal sign. $x=24$

C. Add 6 to both sides of the equal sign. $x=24$

Statement A: Add 6 to Both Sides

If we add 6 to both sides of the equation, we get:

x−6+6=18+6x-6+6=18+6

This simplifies to:

x=24x=24

However, we need to verify if this is the correct method to solve the equation.

Statement B: Subtract 6 from Both Sides

If we subtract 6 from both sides of the equation, we get:

x−6−6=18−6x-6-6=18-6

This simplifies to:

x−12=12x-12=12

Adding 12 to both sides, we get:

x=24x=24

However, we need to verify if this is the correct method to solve the equation.

Statement C: Add 6 to Both Sides

This statement is identical to Statement A, and we have already analyzed it.

Conclusion

Based on our analysis, we can see that both Statements A and B are correct. Adding 6 to both sides of the equation or subtracting 6 from both sides of the equation will result in the same solution, x=24x=24.

However, the correct method to solve the equation is to add 6 to both sides of the equation, as stated in Statement A. This is because we are trying to isolate the variable xx, and adding 6 to both sides will eliminate the constant term, −6-6.

Why Adding 6 to Both Sides is the Correct Method

When we add 6 to both sides of the equation, we are essentially canceling out the constant term, −6-6. This is because −6+6=0-6+6=0, which is a true statement. By adding 6 to both sides, we are creating a new equation that has the same solution as the original equation.

On the other hand, subtracting 6 from both sides of the equation will result in a new equation that has the same solution, but it is not the most straightforward method to solve the equation.

Tips and Tricks for Solving Linear Equations

Here are some tips and tricks for solving linear equations:

  • Always read the equation carefully and identify the variable and the constant term.
  • Use inverse operations to isolate the variable. For example, if the variable is being added to a constant term, use subtraction to eliminate the constant term.
  • Check your work by plugging the solution back into the original equation.
  • Use algebraic properties, such as the commutative and associative properties, to simplify the equation.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By understanding the concept of inverse operations and using algebraic properties, we can solve linear equations with ease. In this article, we analyzed three possible statements for solving the equation $x-6=18$ and determined that adding 6 to both sides of the equation is the correct method. We also provided tips and tricks for solving linear equations, which can be applied to a wide range of mathematical problems.

Final Answer

The final answer is:

Introduction

In our previous article, we explored the concept of solving linear equations and analyzed three possible statements for solving the equation $x-6=18$. In this article, we will address some frequently asked questions related to solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form $ax+b=c$, where aa, bb, and cc are constants, and xx is the variable.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, whereas a quadratic equation is an equation in which the highest power of the variable is 2. For example, $x-6=18$ is a linear equation, while $x^2+4x+4=0$ is a quadratic equation.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable by using inverse operations. For example, if the variable is being added to a constant term, you can use subtraction to eliminate the constant term. You can also use algebraic properties, such as the commutative and associative properties, to simplify the equation.

Q: What is the order of operations for solving linear equations?

A: The order of operations for solving linear equations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my work when solving a linear equation?

A: To check your work, plug the solution back into the original equation and verify that it is true. For example, if you solved the equation $x-6=18$ and got $x=24$, you can plug $x=24$ back into the original equation to verify that it is true:

24−6=1824-6=18

This simplifies to:

18=1818=18

Since this is a true statement, you can be confident that your solution is correct.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Forgetting to use inverse operations to isolate the variable.
  • Not checking your work by plugging the solution back into the original equation.
  • Making algebraic errors, such as forgetting to distribute a negative sign or forgetting to combine like terms.
  • Not using algebraic properties, such as the commutative and associative properties, to simplify the equation.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. For example, if you have the equation $\frac{x}{2}+\frac{3}{4}=5$, you can multiply both sides by 4 to eliminate the fractions:

2x+3=202x+3=20

You can then solve the equation using inverse operations.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By understanding the concept of inverse operations and using algebraic properties, we can solve linear equations with ease. In this article, we addressed some frequently asked questions related to solving linear equations and provided tips and tricks for solving linear equations with fractions.

Final Answer

The final answer is:

  • A linear equation is an equation in which the highest power of the variable is 1.
  • To solve a linear equation, you need to isolate the variable by using inverse operations.
  • The order of operations for solving linear equations is parentheses, exponents, multiplication and division, and addition and subtraction.
  • To check your work, plug the solution back into the original equation and verify that it is true.
  • Some common mistakes to avoid when solving linear equations include forgetting to use inverse operations, not checking your work, making algebraic errors, and not using algebraic properties.