Solve For $x$ In The Equation $x+10=15$.A. $ X = 25 X=25 X = 25 [/tex] B. $x=-5$ C. $x=10$ D. $ X = 5 X=5 X = 5 [/tex]
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Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, $x+10=15$, and provide a step-by-step guide on how to arrive at the correct solution.
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax+b=c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.
The Equation $x+10=15$
The equation $x+10=15$ is a simple linear equation that can be solved using basic algebraic manipulation. To solve for $x$, we need to isolate the variable on one side of the equation.
Step 1: Subtract 10 from Both Sides
To isolate the variable $x$, we need to get rid of the constant term $10$ on the left-hand side of the equation. We can do this by subtracting $10$ from both sides of the equation.
Subtracting $10$ from both sides gives us:
Step 2: Simplify the Right-Hand Side
Now that we have subtracted $10$ from both sides, we can simplify the right-hand side of the equation.
Simplifying the right-hand side gives us:
Conclusion
In conclusion, solving the linear equation $x+10=15$ involves isolating the variable $x$ on one side of the equation. By subtracting $10$ from both sides, we can simplify the equation and arrive at the correct solution, $x=5$.
Answer Key
The correct answer is:
- A. $x=25$: Incorrect
- B. $x=-5$: Incorrect
- C. $x=10$: Incorrect
- D. $x=5$: Correct
Tips and Tricks
When solving linear equations, it's essential to follow the order of operations (PEMDAS):
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
By following these steps and using basic algebraic manipulation, you can solve linear equations with ease.
Real-World Applications
Linear equations have numerous real-world applications in fields such as physics, engineering, economics, and computer science. For example, linear equations can be used to model population growth, electrical circuits, and financial transactions.
Common Mistakes to Avoid
When solving linear equations, it's essential to avoid common mistakes such as:
- Not following the order of operations (PEMDAS)
- Not isolating the variable on one side of the equation
- Not simplifying the equation correctly
- Not checking the solution for validity
By avoiding these common mistakes, you can ensure that your solutions are accurate and reliable.
Conclusion
In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve linear equations with ease and apply them to real-world problems. Remember to follow the order of operations (PEMDAS), isolate the variable on one side of the equation, simplify the equation correctly, and check the solution for validity. With practice and patience, you can become proficient in solving linear equations and tackle more complex mathematical problems with confidence.
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Introduction
In our previous article, we discussed how to solve linear equations using basic algebraic manipulation. In this article, we will provide a Q&A guide to help you better understand the concept of 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. In other words, it is an equation that can be written in the form $ax+b=c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.
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. You can do this by using basic algebraic manipulation, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
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, if you have the equation $2x+3x=5$, you can simplify it by combining the like terms $2x$ and $3x$ to get $5x=5$.
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. For example, the equation $x+2=5$ is a linear equation, while the equation $x^2+2x+1=0$ is a quadratic equation.
Q: How do I check if my solution is valid?
A: To check if your solution is valid, you need to plug it back into the original equation and make sure it is true. For example, if you solve the equation $x+2=5$ and get $x=3$, you can plug $x=3$ back into the original equation to get $3+2=5$, which 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:
- Not following the order of operations (PEMDAS)
- Not isolating the variable on one side of the equation
- Not simplifying the equation correctly
- Not checking the solution for validity
Q: How can I practice solving linear equations?
A: You can practice solving linear equations by working through example problems, such as those found in a math textbook or online resource. You can also try solving linear equations on your own, using a calculator or computer program to check your work.
Q: What are some real-world applications of linear equations?
A: Linear equations have numerous real-world applications in fields such as physics, engineering, economics, and computer science. For example, linear equations can be used to model population growth, electrical circuits, and financial transactions.
Conclusion
In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve linear equations with ease and apply them to real-world problems. Remember to follow the order of operations (PEMDAS), isolate the variable on one side of the equation, simplify the equation correctly, and check the solution for validity. With practice and patience, you can become proficient in solving linear equations and tackle more complex mathematical problems with confidence.