Solve For \[$ A \$\] In The Equation:$\[ 9 = -\frac{7}{10} A - 12 \\]

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Introduction

In mathematics, solving equations is a fundamental concept that involves isolating the variable of interest. In this article, we will focus on solving for ${ a }$ in the given equation: ${ 9 = -\frac{7}{10} a - 12 }$. This equation is a linear equation, and we will use algebraic techniques to isolate the variable ${ a }$.

Understanding the Equation

The given equation is a linear equation in the form of ${ ax + b = c }$, where ${ a }$, ${ b }$, and ${ c }$ are constants. In this case, the equation is ${ 9 = -\frac{7}{10} a - 12 }$. Our goal is to solve for ${ a }$, which means we need to isolate the variable ${ a }$ on one side of the equation.

Isolating the Variable ${ a }$

To isolate the variable ${ a }$, we need to get rid of the constant term on the same side of the equation. In this case, the constant term is ${ -12 }$. We can do this by adding ${ 12 }$ to both sides of the equation. This will keep the equation balanced and allow us to isolate the variable ${ a }$.

${ 9 = -\frac{7}{10} a - 12 }$

Adding ${ 12 }$ to both sides:

${ 9 + 12 = -\frac{7}{10} a - 12 + 12 }$

Simplifying the equation:

${ 21 = -\frac{7}{10} a }$

Eliminating the Fraction

The equation now contains a fraction, which can make it difficult to work with. To eliminate the fraction, we can multiply both sides of the equation by the denominator of the fraction, which is ${ 10 }$. This will allow us to get rid of the fraction and work with whole numbers.

${ 21 = -\frac{7}{10} a }$

Multiplying both sides by ${ 10 }$:

${ 21 \times 10 = -\frac{7}{10} a \times 10 }$

Simplifying the equation:

${ 210 = -7a }$

Solving for ${ a }$

Now that we have eliminated the fraction, we can solve for ${ a }$. To do this, we need to get rid of the negative sign in front of the variable ${ a }$. We can do this by multiplying both sides of the equation by ${ -1 }$.

${ 210 = -7a }$

Multiplying both sides by ${ -1 }$:

${ -210 = 7a }$

Final Step

The final step is to isolate the variable ${ a }$ by dividing both sides of the equation by the coefficient of ${ a }$, which is ${ 7 }$.

${ -210 = 7a }$

Dividing both sides by ${ 7 }$:

${ a = -\frac{210}{7} }$

Simplifying the equation:

${ a = -30 }$

Conclusion

In this article, we solved for ${ a }$ in the equation ${ 9 = -\frac{7}{10} a - 12 }$. We used algebraic techniques to isolate the variable ${ a }$ and eliminate the fraction. The final solution is ${ a = -30 }$. This equation is a linear equation, and solving for ${ a }$ involves isolating the variable and getting rid of the constant term on the same side of the equation.

Frequently Asked Questions

• What is the value of ${ a }$ in the equation ${ 9 = -\frac{7}{10} a - 12 }$?
  • The value of ${ a }$ is ${ -30 }$.
• How do I solve for ${ a }$ in a linear equation?
  • To solve for ${ a }$, you need to isolate the variable ${ a }$ by getting rid of the constant term on the same side of the equation.
• What is the difference between a linear equation and a quadratic equation?
  • A linear equation is an equation in the form of ${ ax + b = c }$, where ${ a }$, ${ b }$, and ${ c }$ are constants. A quadratic equation is an equation in the form of ${ ax^2 + bx + c = 0 }$, where ${ a }$, ${ b }$, and ${ c }$ are constants.

References

• [1] Algebra, 2nd Edition, Michael Artin
• [2] Linear Algebra and Its Applications, 4th Edition, Gilbert Strang
• [3] Calculus, 3rd Edition, Michael Spivak
  

Introduction

In our previous article, we solved for ${ a }$ in the equation ${ 9 = -\frac{7}{10} a - 12 }$. In this article, we will answer some frequently asked questions about solving linear equations. Whether you are a student, a teacher, or just someone who wants to learn more about linear equations, this article is for you.

Q&A

Q: What is a linear equation?

A: A linear equation is an equation in the form of ${ ax + b = c }$, where ${ a }$, ${ b }$, and ${ c }$ are constants. Linear equations can be solved using algebraic techniques.

Q: How do I solve for ${ a }$ in a linear equation?

A: To solve for ${ a }$, you need to isolate the variable ${ a }$ by getting rid of the constant term on the same side of the equation. You can do this by adding or subtracting the same value to both sides of the equation.

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

A: A linear equation is an equation in the form of ${ ax + b = c }$, where ${ a }$, ${ b }$, and ${ c }$ are constants. A quadratic equation is an equation in the form of ${ ax^2 + bx + c = 0 }$, where ${ a }$, ${ b }$, and ${ c }$ are constants. Quadratic equations are more complex and require different techniques to solve.

Q: How do I eliminate fractions in a linear equation?

A: To eliminate fractions in a linear equation, you can multiply both sides of the equation by the denominator of the fraction. This will allow you to get rid of the fraction and work with whole numbers.

Q: What is the order of operations when solving a linear equation?

A: The order of operations when solving a linear equation 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: Can I use a calculator to solve a linear equation?

A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by hand to make sure you understand the solution.

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 isolate the variable ${ a }$
• Not eliminating fractions
• Not following the order of operations
• Not checking your work

Conclusion

In this article, we answered some frequently asked questions about solving linear equations. Whether you are a student, a teacher, or just someone who wants to learn more about linear equations, we hope this article has been helpful. Remember to always follow the order of operations and to check your work to ensure that you understand the solution.

Frequently Asked Questions

• What is the value of ${ a }$ in the equation ${ 9 = -\frac{7}{10} a - 12 }$?
  • The value of ${ a }$ is ${ -30 }$.
• How do I solve for ${ a }$ in a linear equation?
  • To solve for ${ a }$, you need to isolate the variable ${ a }$ by getting rid of the constant term on the same side of the equation.
• What is the difference between a linear equation and a quadratic equation?
  • A linear equation is an equation in the form of ${ ax + b = c }$, where ${ a }$, ${ b }$, and ${ c }$ are constants. A quadratic equation is an equation in the form of ${ ax^2 + bx + c = 0 }$, where ${ a }$, ${ b }$, and ${ c }$ are constants.

References

• [1] Algebra, 2nd Edition, Michael Artin
• [2] Linear Algebra and Its Applications, 4th Edition, Gilbert Strang
• [3] Calculus, 3rd Edition, Michael Spivak