What Is The Solution To This Equation?$\[ X - 17 = -5 \\]A. $\[ X = -12 \\]B. $\[ X = 12 \\]C. $\[ X = 22 \\]D. $\[ X = -22 \\]

Understanding the Equation

The given equation is a linear equation in the form of $x - 17 = -5$. To solve for the value of $x$, we need to isolate the variable $x$ on one side of the equation. This can be done by adding or subtracting the same value to both sides of the equation.

Step 1: Add 17 to Both Sides

To isolate the variable $x$, we need to get rid of the constant term $-17$ on the left side of the equation. We can do this by adding $17$ to both sides of the equation. This will result in:

$x - 17 + 17 = -5 + 17$

Simplifying the Equation

When we add $17$ to both sides of the equation, the $-17$ on the left side cancels out, leaving us with just $x$. On the right side, $-5 + 17$ equals $12$. Therefore, the simplified equation is:

$x = 12$

Checking the Answer Choices

Now that we have solved for the value of $x$, we can check our answer against the given options. The correct solution is:

$x = 12$

This matches option B.

Conclusion

In conclusion, the solution to the equation $x - 17 = -5$ is $x = 12$. This can be verified by adding $17$ to both sides of the equation, resulting in $x = 12$. Therefore, the correct answer is option B.

Frequently Asked Questions

• What is the solution to the equation $x - 17 = -5$?
• How do I solve for the value of $x$ in a linear equation?
• What is the correct answer among the given options?

Answering the FAQs

• The solution to the equation $x - 17 = -5$ is $x = 12$.
• To solve for the value of $x$ in a linear equation, you need to isolate the variable $x$ on one side of the equation by adding or subtracting the same value to both sides.
• The correct answer among the given options is option B, which is $x = 12$.

Additional Tips and Tricks

• When solving linear equations, make sure to isolate the variable $x$ on one side of the equation.
• Use addition and subtraction to get rid of constant terms on the left side of the equation.
• Check your answer against the given options to ensure you have the correct solution.

Real-World Applications

• Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications, such as:
• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the distance between two points

Conclusion

In conclusion, solving linear equations is a crucial skill in mathematics that has numerous real-world applications. By following the steps outlined in this article, you can easily solve linear equations and find the correct solution. Remember to isolate the variable $x$ on one side of the equation and check your answer against the given options to ensure you have the correct solution.

Q&A: Solving Linear Equations

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It is a simple equation that can be solved by isolating the variable on one side of the equation.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation by adding or subtracting the same value to both sides. You can also multiply or divide both sides by the same non-zero value to isolate the variable.

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

A: When solving a linear equation, you should follow the order of operations (PEMDAS):

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 handle fractions when solving a linear equation?

A: When solving a linear equation with fractions, you can multiply both sides of the equation by the denominator of the fraction to eliminate the fraction. This will allow you to solve for 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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. Quadratic equations are more complex and require different techniques to solve.

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 answer by plugging it back into the original equation to ensure that it is correct.

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

A: To check your answer, plug the value you found for the variable back into the original equation. If the equation is true, then your answer 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 isolate the variable on one side of the equation
• Not following the order of operations
• Not checking your answer
• Making arithmetic errors

Q: Can I use algebraic methods to solve linear equations?

A: Yes, you can use algebraic methods to solve linear equations. Some common algebraic methods include:

• Adding or subtracting the same value to both sides of the equation
• Multiplying or dividing both sides of the equation by the same non-zero value
• Using inverse operations to isolate the variable

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to identify the inverse operation of the operation that is being performed on the variable. For example, if the equation is $x + 3 = 7$, the inverse operation of addition is subtraction. Therefore, you can subtract 3 from both sides of the equation to isolate the variable.

Q: Can I use graphing to solve linear equations?

A: Yes, you can use graphing to solve linear equations. By graphing the equation on a coordinate plane, you can find the point of intersection between the two lines, which represents the solution to the equation.

Q: What are some real-world applications of linear equations?

A: Linear equations have numerous real-world applications, including:

• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the distance between two points
• Modeling population growth and decline
• Solving problems in physics and engineering

Q: Can I use linear equations to solve systems of equations?

A: Yes, you can use linear equations to solve systems of equations. By using substitution or elimination methods, you can solve for the variables in a system of linear equations.

Q: How do I use substitution to solve a system of linear equations?

A: To use substitution to solve a system of linear equations, you need to solve one of the equations for one of the variables and then substitute that expression into the other equation. This will allow you to solve for the other variable.

Q: Can I use linear equations to solve quadratic equations?

A: No, you cannot use linear equations to solve quadratic equations. Quadratic equations require different techniques to solve, such as factoring or using the quadratic formula.

Q: What are some common types of linear equations?

A: Some common types of linear equations include:

• Linear equations with one variable
• Linear equations with two variables
• Linear equations with fractions
• Linear equations with decimals
• Linear equations with negative coefficients

Q: Can I use linear equations to solve inequalities?

A: Yes, you can use linear equations to solve inequalities. By using the same techniques as solving linear equations, you can solve for the variable in an inequality.

Q: How do I use linear equations to solve systems of inequalities?

A: To use linear equations to solve systems of inequalities, you need to use the same techniques as solving systems of linear equations. By using substitution or elimination methods, you can solve for the variables in a system of inequalities.

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

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

• Forgetting to isolate the variable on one side of the equation
• Not following the order of operations
• Not checking your answer
• Making arithmetic errors

Q: Can I use linear equations to solve systems of linear inequalities?

A: Yes, you can use linear equations to solve systems of linear inequalities. By using the same techniques as solving systems of linear equations, you can solve for the variables in a system of linear inequalities.

Q: How do I use linear equations to solve systems of linear inequalities with multiple variables?

A: To use linear equations to solve systems of linear inequalities with multiple variables, you need to use the same techniques as solving systems of linear equations. By using substitution or elimination methods, you can solve for the variables in a system of linear inequalities with multiple variables.

Q: What are some real-world applications of systems of linear equations?

A: Systems of linear equations have numerous real-world applications, including:

• Modeling population growth and decline
• Solving problems in physics and engineering
• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the distance between two points

Q: Can I use linear equations to solve systems of linear inequalities with multiple variables and fractions?

A: Yes, you can use linear equations to solve systems of linear inequalities with multiple variables and fractions. By using the same techniques as solving systems of linear equations, you can solve for the variables in a system of linear inequalities with multiple variables and fractions.

Q: How do I use linear equations to solve systems of linear inequalities with multiple variables and decimals?

A: To use linear equations to solve systems of linear inequalities with multiple variables and decimals, you need to use the same techniques as solving systems of linear equations. By using substitution or elimination methods, you can solve for the variables in a system of linear inequalities with multiple variables and decimals.

Q: What are some common types of systems of linear equations?

A: Some common types of systems of linear equations include:

• Systems of linear equations with one variable
• Systems of linear equations with two variables
• Systems of linear equations with fractions
• Systems of linear equations with decimals
• Systems of linear equations with negative coefficients

Q: Can I use linear equations to solve systems of linear inequalities with multiple variables and negative coefficients?

A: Yes, you can use linear equations to solve systems of linear inequalities with multiple variables and negative coefficients. By using the same techniques as solving systems of linear equations, you can solve for the variables in a system of linear inequalities with multiple variables and negative coefficients.

Q: How do I use linear equations to solve systems of linear inequalities with multiple variables and mixed numbers?

A: To use linear equations to solve systems of linear inequalities with multiple variables and mixed numbers, you need to use the same techniques as solving systems of linear equations. By using substitution or elimination methods, you can solve for the variables in a system of linear inequalities with multiple variables and mixed numbers.

Q: What are some real-world applications of systems of linear inequalities?

A: Systems of linear inequalities have numerous real-world applications, including:

• Modeling population growth and decline
• Solving problems in physics and engineering
• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the distance between two points

Q: Can I use linear equations to solve systems of linear inequalities with multiple variables and complex numbers?

A: Yes, you can use linear equations to solve systems of linear inequalities with multiple variables and complex numbers. By using the same techniques as solving systems of linear equations, you can solve for the variables in a system of linear inequalities with multiple variables and complex numbers.

Q: How do I use linear equations to solve systems of linear inequalities with multiple variables and imaginary numbers?

A: To use linear equations to solve systems of linear inequalities with multiple variables and imaginary numbers, you need to use the same techniques as solving systems of linear equations. By using substitution or elimination methods, you can solve for the variables in a system of linear inequalities with multiple variables and imaginary numbers.

Q: What are some common types of systems of linear inequalities?

A: Some common types of systems of linear inequalities include:

• Systems of linear inequalities with one variable
• Systems of linear inequalities