Solve For { X $}$ In The Equation:${ 8.4x + 9 = 25 }$

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Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving a linear equation with a decimal coefficient, specifically the equation ${ 8.4x + 9 = 25 }$. This equation involves a decimal coefficient, which can make it more challenging to solve. However, with the correct steps and techniques, we can easily isolate the variable and find the value of $x$.

Understanding the Equation

The given equation is ${ 8.4x + 9 = 25 }$. To solve for $x$, we need to isolate the variable on one side of the equation. The equation involves a decimal coefficient, which is $8.4$. This coefficient is multiplied by the variable $x$, and then there is a constant term $9$ on the left side of the equation. The right side of the equation is a constant value, which is $25$.

Step 1: Subtract 9 from Both Sides

To isolate the variable, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting $9$ from both sides of the equation. This will give us:

${ 8.4x + 9 - 9 = 25 - 9 }$

Simplifying the equation, we get:

${ 8.4x = 16 }$

Step 2: Divide Both Sides by 8.4

Now that we have isolated the variable term, we need to get rid of the coefficient $8.4$. We can do this by dividing both sides of the equation by $8.4$. This will give us:

${ \frac{8.4x}{8.4} = \frac{16}{8.4} }$

Simplifying the equation, we get:

${ x = \frac{16}{8.4} }$

Calculating the Value of x

To find the value of $x$, we need to divide $16$ by $8.4$. This will give us:

${ x = 1.90476 }$

Rounding the value to two decimal places, we get:

${ x = 1.90 }$

Conclusion

In this article, we solved a linear equation with a decimal coefficient, specifically the equation ${ 8.4x + 9 = 25 }$. We used the steps of subtracting $9$ from both sides and then dividing both sides by $8.4$ to isolate the variable and find the value of $x$. The final value of $x$ is $1.90$. This equation is a simple example of how to solve linear equations with decimal coefficients.

Tips and Tricks

When solving linear equations with decimal coefficients, it is essential to follow the correct steps and techniques. Here are some tips and tricks to keep in mind:

• Always start by isolating the variable term on one side of the equation.
• Use the correct order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
• When dividing both sides of the equation by a decimal coefficient, make sure to round the value to the correct number of decimal places.
• Always check your work by plugging the value of $x$ back into the original equation to ensure that it is true.

Real-World Applications

Solving linear equations with decimal coefficients has many real-world applications. Here are a few examples:

• In finance, linear equations with decimal coefficients are used to calculate interest rates and investment returns.
• In science, linear equations with decimal coefficients are used to model population growth and chemical reactions.
• In engineering, linear equations with decimal coefficients are used to design and optimize systems.

Final Thoughts

Solving linear equations with decimal coefficients is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. By following the correct steps and techniques, we can easily solve linear equations with decimal coefficients and find the value of $x$. Whether it's in finance, science, or engineering, linear equations with decimal coefficients have many real-world applications, and it's essential to understand how to solve them.

References

• [1] "Linear Equations" by Math Open Reference. Retrieved from https://www.mathopenref.com/linearequations.html
• [2] "Solving Linear Equations" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7f0b-solve-linear-equations
• [3] "Decimal Coefficients" by Math Is Fun. Retrieved from https://www.mathisfun.com/numbers/decimal-coefficients.html

Related Topics

• Solving Quadratic Equations
• Solving Systems of Linear Equations
• Linear Inequalities

Further Reading

• Linear Algebra
• Calculus
• Differential Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable is 1.
• Decimal Coefficient: A coefficient that is a decimal number.
• Isolate the Variable: To get the variable term on one side of the equation by itself.
• PEMDAS: A mnemonic device that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, which is used to remember the correct order of operations.
  

Frequently Asked Questions

Q: What is a linear equation with a decimal coefficient?

A: A linear equation with a decimal coefficient is an equation in which the coefficient of the variable is a decimal number. For example, the equation $8.4x + 9 = 25$ is a linear equation with a decimal coefficient.

Q: How do I solve a linear equation with a decimal coefficient?

A: To solve a linear equation with a decimal coefficient, you need to isolate the variable term on one side of the equation by itself. You can do this by subtracting the constant term from both sides of the equation and then dividing both sides by the decimal coefficient.

Q: What is the correct order of operations when solving a linear equation with a decimal coefficient?

A: The correct order of operations when solving a linear equation with a decimal coefficient is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

Q: How do I round the value of x when it is a decimal?

A: When the value of x is a decimal, you should round it to the correct number of decimal places. For example, if the value of x is 1.90476, you should round it to two decimal places, which is 1.90.

Q: What are some real-world applications of solving linear equations with decimal coefficients?

A: Solving linear equations with decimal coefficients has many real-world applications, including finance, science, and engineering. For example, in finance, linear equations with decimal coefficients are used to calculate interest rates and investment returns. In science, linear equations with decimal coefficients are used to model population growth and chemical reactions. In engineering, linear equations with decimal coefficients are used to design and optimize systems.

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

A: To check your work when solving a linear equation with a decimal coefficient, you should plug the value of x back into the original equation to ensure that it is true. If the equation is true, then you have solved the equation correctly.

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

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

• Not following the correct order of operations
• Not isolating the variable term on one side of the equation
• Not rounding the value of x to the correct number of decimal places
• Not checking your work by plugging the value of x back into the original equation

Q: How do I use technology to solve linear equations with decimal coefficients?

A: There are many online tools and calculators that can help you solve linear equations with decimal coefficients. For example, you can use a graphing calculator or a computer algebra system to solve linear equations with decimal coefficients.

Q: What are some advanced topics related to solving linear equations with decimal coefficients?

A: Some advanced topics related to solving linear equations with decimal coefficients include:

• Solving systems of linear equations with decimal coefficients
• Solving linear inequalities with decimal coefficients
• Using linear algebra to solve linear equations with decimal coefficients

Additional Resources

• Linear Equations
• Decimal Coefficients
• Linear Algebra
• Calculus
• Differential Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable is 1.
• Decimal Coefficient: A coefficient that is a decimal number.
• Isolate the Variable: To get the variable term on one side of the equation by itself.
• PEMDAS: A mnemonic device that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, which is used to remember the correct order of operations.

Related Topics

• Solving Quadratic Equations
• Solving Systems of Linear Equations
• Linear Inequalities

Further Reading

• Linear Algebra
• Calculus
• Differential Equations

Final Thoughts

Solving linear equations with decimal coefficients is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. By following the correct steps and techniques, we can easily solve linear equations with decimal coefficients and find the value of x. Whether it's in finance, science, or engineering, linear equations with decimal coefficients have many real-world applications, and it's essential to understand how to solve them.