What Is The Solution To This Equation?$\[ X - 17 = -5 \\]A. \[$ X = -12 \$\]B. \[$ X = 12 \$\]C. \[$ X = -22 \$\]D. \[$ X = 22 \$\]
Introduction
In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. Equations are statements that express the equality of two mathematical expressions. In this article, we will focus on solving a simple linear equation to find the value of the unknown variable x.
The Equation
The given equation is:
x - 17 = -5
Understanding the Equation
To solve this equation, we need to isolate the variable x. The equation is a linear equation, which means it has a single variable and a constant term. The variable x is being subtracted by 17, and the result is equal to -5.
Step 1: Add 17 to Both Sides
To isolate the variable x, we need to get rid of the constant term -17. We can do this by adding 17 to both sides of the equation. This will cancel out the -17 on the left side of the equation.
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.
x = 12
Conclusion
Therefore, the solution to the equation x - 17 = -5 is x = 12. This means that the value of the unknown variable x is 12.
Why is this the Correct Solution?
To verify that x = 12 is the correct solution, we can substitute this value back into the original equation and check if it holds true.
x - 17 = -5 12 - 17 = -5 -5 = -5
As we can see, the equation holds true when x = 12. This confirms that x = 12 is indeed the correct solution to the equation.
What if the Equation was Different?
If the equation was different, such as x + 17 = 5, the solution would be different as well. In this case, we would need to isolate the variable x by subtracting 17 from both sides of the equation.
x + 17 - 17 = 5 - 17 x = -12
In this case, the solution to the equation x + 17 = 5 is x = -12.
Conclusion
In conclusion, solving equations is an essential skill in mathematics that helps us find the value of unknown variables. By following the steps outlined in this article, we can solve simple linear equations and find the correct solution. Whether the equation is x - 17 = -5 or x + 17 = 5, the solution will depend on the specific equation and the steps we take to isolate the variable x.
Common Mistakes to Avoid
When solving equations, there are several common mistakes to avoid. These include:
- Not following the order of operations: When solving equations, it's essential to follow the order of operations (PEMDAS) to ensure that we perform the calculations correctly.
- Not isolating the variable: To solve an equation, we need to isolate the variable x. This means getting rid of any constant terms that are attached to the variable.
- Not checking the solution: Before accepting a solution, it's essential to check that it satisfies the original equation.
Tips for Solving Equations
Here are some tips for solving equations:
- Read the equation carefully: Before starting to solve the equation, read it carefully to understand what it's asking for.
- Use inverse operations: To isolate the variable x, use inverse operations such as addition and subtraction to get rid of any constant terms.
- Check the solution: Before accepting a solution, check that it satisfies the original equation.
Conclusion
Q: What is an equation?
A: An equation is a statement that expresses the equality of two mathematical expressions. It is a way of representing a relationship between variables and constants.
Q: What is a variable?
A: A variable is a letter or symbol that represents a value that can change. In an equation, the variable is the unknown value that we are trying to solve for.
Q: What is a constant?
A: A constant is a value that does not change. In an equation, constants are numbers that are attached to the variable.
Q: How do I solve an equation?
A: To solve an equation, you need to isolate the variable by getting rid of any constant terms that are attached to it. You can do this by using inverse operations such as addition and subtraction.
Q: What is an inverse operation?
A: An inverse operation is an operation that "reverses" another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.
Q: How do I use inverse operations to solve an equation?
A: To use inverse operations to solve an equation, you need to identify the operation that is being performed on the variable and then perform the inverse operation to get rid of the constant term.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
Q: Why is it important to follow the order of operations?
A: Following the order of operations is important because it ensures that you perform the operations in the correct order and get the correct solution.
Q: What is a linear equation?
A: A linear equation is an equation that has a single variable and a constant term. It is a straight line on a graph.
Q: What is a quadratic equation?
A: A quadratic equation is an equation that has a squared variable and a constant term. It is a parabola on a graph.
Q: How do I solve a quadratic equation?
A: To solve a quadratic equation, you need to use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Q: What is the quadratic formula?
A: The quadratic formula is a formula that is used to solve quadratic equations. It is a way of finding the solutions to a quadratic equation.
Q: Why is it important to check the solution?
A: Checking the solution is important because it ensures that the solution you found is correct and satisfies the original equation.
Q: How do I check the solution?
A: To check the solution, you need to substitute the solution back into the original equation and check if it holds true.
Conclusion
In conclusion, solving equations is an essential skill in mathematics that helps us find the value of unknown variables. By following the steps outlined in this article and avoiding common mistakes, we can solve simple linear equations and find the correct solution. Whether the equation is x - 17 = -5 or x + 17 = 5, the solution will depend on the specific equation and the steps we take to isolate the variable x.