Solve For $g$.$\frac{g}{12} = -10$

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Introduction

Solving for a variable in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable to find its value. In this article, we will focus on solving for the variable $g$ in the equation $\frac{g}{12} = -10$. This equation involves a fraction, and we will use algebraic techniques to isolate the variable $g$.

Understanding the Equation

The given equation is $\frac{g}{12} = -10$. This equation states that the ratio of $g$ to 12 is equal to -10. To solve for $g$, we need to isolate the variable $g$ on one side of the equation.

Isolating the Variable $g$

To isolate the variable $g$, we can start by multiplying both sides of the equation by 12. This will eliminate the fraction and allow us to work with a simpler equation.

$\frac{g}{12} = -10$

Multiplying both sides by 12:

$g = -10 \times 12$

Solving for $g$

Now that we have eliminated the fraction, we can solve for $g$ by multiplying -10 and 12.

$g = -10 \times 12$

$g = -120$

Conclusion

In this article, we have solved for the variable $g$ in the equation $\frac{g}{12} = -10$. We started by understanding the equation and then used algebraic techniques to isolate the variable $g$. By multiplying both sides of the equation by 12, we were able to eliminate the fraction and solve for $g$. The final value of $g$ is -120.

Real-World Applications

Solving for a variable in an equation is a fundamental concept in mathematics, and it has numerous real-world applications. In physics, for example, the equation $\frac{g}{12} = -10$ can be used to model the motion of an object under the influence of gravity. In economics, the equation can be used to model the relationship between two variables, such as the price of a commodity and its demand.

Tips and Tricks

When solving for a variable in an equation, it is essential to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any 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.

By following the order of operations, you can ensure that you are solving for the variable correctly.

Common Mistakes

When solving for a variable in an equation, there are several common mistakes to avoid:

1. Not following the order of operations (PEMDAS).
2. Not isolating the variable correctly.
3. Not checking the solution for validity.

By avoiding these common mistakes, you can ensure that you are solving for the variable correctly.

Final Thoughts

Solving for a variable in an equation is a fundamental concept in mathematics, and it has numerous real-world applications. By understanding how to isolate the variable and following the order of operations (PEMDAS), you can solve for the variable correctly. Remember to avoid common mistakes and check your solution for validity.

Frequently Asked Questions

Q: What is the value of $g$ in the equation $\frac{g}{12} = -10$?

A: The value of $g$ is -120.

Q: How do I solve for a variable in an equation?

A: To solve for a variable in an equation, you need to isolate the variable on one side of the equation. You can do this by using algebraic techniques, such as multiplying both sides of the equation by a constant.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which you should evaluate mathematical expressions. The rules are:

1. Parentheses: Evaluate any 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: What are some common mistakes to avoid when solving for a variable in an equation?

A: Some common mistakes to avoid when solving for a variable in an equation include:

1. Not following the order of operations (PEMDAS).
2. Not isolating the variable correctly.
3. Not checking the solution for validity.

By avoiding these common mistakes, you can ensure that you are solving for the variable correctly.

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Q&A: Solving for $g$.$\frac{g}{12} = -10$

Q: What is the value of $g$ in the equation $\frac{g}{12} = -10$?

A: The value of $g$ is -120.

Q: How do I solve for a variable in an equation?

A: To solve for a variable in an equation, you need to isolate the variable on one side of the equation. You can do this by using algebraic techniques, such as multiplying both sides of the equation by a constant.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which you should evaluate mathematical expressions. The rules are:

1. Parentheses: Evaluate any 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: What are some common mistakes to avoid when solving for a variable in an equation?

A: Some common mistakes to avoid when solving for a variable in an equation include:

1. Not following the order of operations (PEMDAS).
2. Not isolating the variable correctly.
3. Not checking the solution for validity.

Q: How do I check if my solution is valid?

A: To check if your solution is valid, you need to plug the solution back into the original equation and verify that it is true. If the solution is not valid, you need to re-evaluate your work and try again.

Q: What is the difference between a variable and a constant?

A: A variable is a value that can change, while a constant is a value that remains the same. In the equation $\frac{g}{12} = -10$, $g$ is a variable and 12 and -10 are constants.

Q: How do I simplify an equation?

A: To simplify an equation, you need to combine like terms and eliminate any unnecessary operations. For example, the equation $2x + 3x = 5x + 2$ can be simplified by combining the like terms $2x$ and $3x$ to get $5x$.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal, while an expression is a mathematical statement that contains variables and constants. For example, the equation $2x + 3 = 5$ is an equation, while the expression $2x + 3$ is an expression.

Q: How do I solve a system of equations?

A: To solve a system of equations, you need to find the values of the variables that satisfy all of the equations in the system. You can do this by using algebraic techniques, such as substitution and elimination.

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, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation $2x + 3 = 5$ is a linear equation, while the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.

Q: How do I graph an equation?

A: To graph an equation, you need to plot the points that satisfy the equation and connect them with a line. You can use a graphing calculator or a graphing software to help you graph the equation.

Q: What is the difference between a function and a relation?

A: A function is a relation in which each input corresponds to exactly one output, while a relation is a set of ordered pairs that satisfy a certain condition. For example, the function $f(x) = 2x + 3$ is a function, while the relation $\{(1,2),(2,3),(3,4)\}$ is a relation.

Q: How do I find the domain and range of a function?

A: To find the domain and range of a function, you need to identify the set of input values that correspond to the function and the set of output values that correspond to the function. You can use a graph or a table to help you find the domain and range of the function.

Q: What is the difference between a rational function and an irrational function?

A: A rational function is a function that can be expressed as a ratio of two polynomials, while an irrational function is a function that cannot be expressed as a ratio of two polynomials. For example, the function $f(x) = \frac{2x + 3}{x - 1}$ is a rational function, while the function $f(x) = \sqrt{x}$ is an irrational function.

Q: How do I find the inverse of a function?

A: To find the inverse of a function, you need to swap the input and output values of the function and solve for the new input value. You can use a graph or a table to help you find the inverse of the function.

Q: What is the difference between a one-to-one function and a many-to-one function?

A: A one-to-one function is a function in which each input corresponds to exactly one output, while a many-to-one function is a function in which each input corresponds to more than one output. For example, the function $f(x) = 2x + 3$ is a one-to-one function, while the function $f(x) = x^2$ is a many-to-one function.

Q: How do I find the derivative of a function?

A: To find the derivative of a function, you need to use the power rule, the product rule, and the quotient rule to differentiate the function. You can use a graph or a table to help you find the derivative of the function.

Q: What is the difference between a function and a relation?

A: A function is a relation in which each input corresponds to exactly one output, while a relation is a set of ordered pairs that satisfy a certain condition. For example, the function $f(x) = 2x + 3$ is a function, while the relation $\{(1,2),(2,3),(3,4)\}$ is a relation.

Q: How do I find the integral of a function?

A: To find the integral of a function, you need to use the power rule, the product rule, and the quotient rule to integrate the function. You can use a graph or a table to help you find the integral of the function.

Q: What is the difference between a definite integral and an indefinite integral?

A: A definite integral is an integral that has a specific upper and lower bound, while an indefinite integral is an integral that does not have a specific upper and lower bound. For example, the definite integral $\int_{0}^{1} x^2 dx$ is a definite integral, while the indefinite integral $\int x^2 dx$ is an indefinite integral.

Q: How do I find the area under a curve?

A: To find the area under a curve, you need to use the definite integral to integrate the function and find the area between the curve and the x-axis. You can use a graph or a table to help you find the area under the curve.

Q: What is the difference between a function and a relation?

A: A function is a relation in which each input corresponds to exactly one output, while a relation is a set of ordered pairs that satisfy a certain condition. For example, the function $f(x) = 2x + 3$ is a function, while the relation $\{(1,2),(2,3),(3,4)\}$ is a relation.

Q: How do I find the domain and range of a function?

A: To find the domain and range of a function, you need to identify the set of input values that correspond to the function and the set of output values that correspond to the function. You can use a graph or a table to help you find the domain and range of the function.

Q: What is the difference between a rational function and an irrational function?

A: A rational function is a function that can be expressed as a ratio of two polynomials, while an irrational function is a function that cannot be expressed as a ratio of two polynomials. For example, the function $f(x) = \frac{2x + 3}{x - 1}$ is a rational function, while the function $f(x) = \sqrt{x}$ is an irrational function.

Q: How do I find the inverse of a function?

A: To find the inverse of a function, you need to swap the input and output values of the function and solve for the new input value. You can use a graph or a table to help you find the inverse of the function.

Q: What is the difference between a one-to-one function and a many-to-one function?

A: A one-to-one function is a function in which each input corresponds to exactly one output, while a many-to-one function is a function in which each input corresponds to more than one output. For example, the function $f(x) = 2x + 3$ is a one-to-one function, while the function $f(x) = x^2$ is a many-to-one function.

Q: How do I find the derivative of a function?

A: To find the derivative of a function, you need to use the power rule, the product rule,