What Is The Solution To This Equation?$\[ X - 8 = 15 \\]A. \[$ X = 7 \$\] B. \[$ X = 17 \$\] C. \[$ X = 23 \$\] D. \[$ X = 13 \$\]

Understanding the Equation

The given equation is a linear equation in the form of $x - 8 = 15$. 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 8 to Both Sides of the Equation

To isolate the variable $x$, we need to get rid of the constant term $-8$ on the left side of the equation. We can do this by adding $8$ to both sides of the equation. This will result in:

$x - 8 + 8 = 15 + 8$

Simplifying the Equation

When we add $8$ to both sides of the equation, the $-8$ on the left side cancels out, and we are left with:

$x = 23$

Checking the Solution

To verify that the solution is correct, we can substitute $x = 23$ back into the original equation and check if it is true.

$x - 8 = 15$ $23 - 8 = 15$ $15 = 15$

Since the equation holds true, we can conclude that the solution is correct.

Conclusion

The solution to the equation $x - 8 = 15$ is $x = 23$. This can be verified by substituting the solution back into the original equation and checking if it is true.

Answer

The correct answer is:

C. $x = 23$

Why is this the Correct Answer?

This is the correct answer because when we add $8$ to both sides of the equation, we get $x = 23$. This is the only solution that satisfies the equation.

What if I Choose a Different Answer?

If you choose a different answer, such as $x = 7$, $x = 17$, or $x = 13$, you will find that it does not satisfy the equation. For example, if you substitute $x = 7$ into the equation, you get:

$7 - 8 = 15$ $-1 \neq 15$

Since $-1$ is not equal to $15$, we can conclude that $x = 7$ is not the correct solution.

Tips for Solving Linear Equations

When solving linear equations, it is essential to isolate the variable on one side of the equation. This can be done by adding or subtracting the same value to both sides of the equation. In this case, we added $8$ to both sides of the equation to get rid of the constant term $-8$.

Common Mistakes to Avoid

One common mistake to avoid when solving linear equations is to forget to add or subtract the same value to both sides of the equation. This can result in an incorrect solution. For example, if you forget to add $8$ to both sides of the equation, you will get:

$x - 8 = 15$ $x = 23$

However, this is not the correct solution. The correct solution is $x = 23$, which can be obtained by adding $8$ to both sides of the equation.

Conclusion

In conclusion, the solution to the equation $x - 8 = 15$ is $x = 23$. This can be verified by substituting the solution back into the original equation and checking if it is true. When solving linear equations, it is essential to isolate the variable on one side of the equation by adding or subtracting the same value to both sides of the equation.

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. This can be done by adding or subtracting the same value to both sides of the equation.

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 any expressions inside parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: 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 need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers.

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

A: To check if your solution is correct, you need to substitute the solution back into the original equation and check if it is true.

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 add or subtract the same value to both sides of the equation.
• Not isolating the variable on one side of the equation.
• Not checking if the solution is correct.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it is essential to understand the steps involved in solving the equation and to check if the solution is correct.

Q: How do I solve a linear equation with multiple variables?

A: To solve a linear equation with multiple variables, you need to isolate one variable on one side of the equation and then substitute the expression into the other 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.

Q: Can I solve a linear equation with a negative coefficient?

A: Yes, you can solve a linear equation with a negative coefficient. The steps involved in solving the equation are the same as for a linear equation with a positive 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 follow the same steps as for a linear equation with a fraction coefficient.

Q: Can I use a graphing calculator to solve linear equations?

A: Yes, you can use a graphing calculator to solve linear equations. However, it is essential to understand the steps involved in solving the equation and to check if the solution is correct.

Q: How do I solve a linear equation with a variable in the denominator?

A: To solve a linear equation with a variable in the denominator, you need to eliminate the variable in the denominator by multiplying both sides of the equation by the variable.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation with one or more variables, while a system of linear equations is a set of two or more linear equations with the same variables.

Q: Can I solve a system of linear equations using substitution?

A: Yes, you can solve a system of linear equations using substitution. This involves substituting the expression for one variable into the other equation.

Q: How do I solve a system of linear equations using elimination?

A: To solve a system of linear equations using elimination, you need to add or subtract the equations to eliminate one variable.

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

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a nonlinear equation is an equation in which the highest power of the variable(s) is greater than 1.

Q: Can I solve a nonlinear equation using algebraic methods?

A: No, you cannot solve a nonlinear equation using algebraic methods. Nonlinear equations require numerical methods or graphical methods to solve.

Q: How do I solve a nonlinear equation using numerical methods?

A: To solve a nonlinear equation using numerical methods, you need to use a numerical solver or a computer program to find the solution.

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

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a differential equation is an equation that involves the derivative of a function.

Q: Can I solve a differential equation using algebraic methods?

A: No, you cannot solve a differential equation using algebraic methods. Differential equations require numerical methods or analytical methods to solve.

Q: How do I solve a differential equation using numerical methods?

A: To solve a differential equation using numerical methods, you need to use a numerical solver or a computer program to find the solution.

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

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a partial differential equation is an equation that involves the partial derivatives of a function.

Q: Can I solve a partial differential equation using algebraic methods?

A: No, you cannot solve a partial differential equation using algebraic methods. Partial differential equations require numerical methods or analytical methods to solve.

Q: How do I solve a partial differential equation using numerical methods?

A: To solve a partial differential equation using numerical methods, you need to use a numerical solver or a computer program to find the solution.