Solve The Equation Below For $x$.$0.5(x + 7) + 9 = 43$Respond In The Space Provided.$ X = □ X = \square X = □ [/tex]
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 specific linear equation, $0.5(x + 7) + 9 = 43$, and provide a step-by-step guide on how to isolate the variable $x$.
Understanding the Equation
Before we dive into solving the equation, let's break it down and understand its components. The equation is in the form of a linear equation, which is a polynomial equation of degree one. The general form of a linear equation is $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.
In our equation, $0.5(x + 7) + 9 = 43$, we have:
Step 1: Distribute the Coefficient
The first step in solving the equation is to distribute the coefficient $0.5$ to the terms inside the parentheses. This will give us:
Step 2: Combine Like Terms
Next, we combine the like terms on the left-hand side of the equation. In this case, we can combine the constants $3.5$ and $9$ to get:
Step 3: Isolate the Variable
Now, we need to isolate the variable $x$. To do this, we subtract $12.5$ from both sides of the equation:
Step 4: Solve for x
Finally, we solve for $x$ by dividing both sides of the equation by $0.5$:
Conclusion
In this article, we solved the linear equation $0.5(x + 7) + 9 = 43$ using a step-by-step approach. We distributed the coefficient, combined like terms, isolated the variable, and finally solved for $x$. The solution to the equation is $x = 61$.
Tips and Tricks
- When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the calculations correctly.
- When distributing coefficients, make sure to multiply each term inside the parentheses by the coefficient.
- When combining like terms, make sure to combine the coefficients and the constants separately.
- When isolating the variable, make sure to add or subtract the same value from both sides of the equation.
Practice Problems
Try solving the following linear equations using the steps outlined in this article:
References
About the Author
Introduction
In our previous article, we solved a linear equation step-by-step and provided a guide on how to isolate the variable. However, we know that practice makes perfect, and the best way to learn is by doing. In this article, we will provide a Q&A guide to help you practice solving linear equations.
Q1: What is a linear equation?
A linear equation is a polynomial equation of degree one, which means it has no squared or higher-order terms. The general form of a linear equation is $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.
Q2: How do I solve a linear equation?
To solve a linear equation, you need to follow these steps:
- Distribute the coefficient to the terms inside the parentheses.
- Combine like terms on the left-hand side of the equation.
- Isolate the variable by adding or subtracting the same value from both sides of the equation.
- Solve for the variable by dividing both sides of the equation by the coefficient.
Q3: What is the order of operations (PEMDAS)?
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.
Q4: How do I distribute a coefficient?
To distribute a coefficient, you need to multiply each term inside the parentheses by the coefficient. For example, if you have the equation $2(x + 3) = 10$, you would distribute the coefficient 2 to the terms inside the parentheses like this:
Q5: What is the difference between a linear equation and a quadratic equation?
A linear equation is a polynomial equation of degree one, while a quadratic equation is a polynomial equation of degree two. The general form of a linear equation is $ax + b = c$, while the general form of a quadratic equation is $ax^2 + bx + c = 0$.
Q6: Can I use a calculator to solve a linear equation?
Yes, you can use a calculator to solve a linear equation. However, it's essential to understand the steps involved in solving the equation, as using a calculator without understanding the concept can lead to confusion and mistakes.
Q7: How do I check my answer?
To check your answer, you need to plug the solution back into the original equation and verify that it's true. For example, if you solved the equation $2x + 3 = 7$ and got $x = 2$, you would plug $x = 2$ back into the original equation like this:
Since the equation is true, your solution is correct.
Q8: What are some common mistakes to avoid when solving linear equations?
Some common mistakes to avoid when solving linear equations include:
- Not distributing the coefficient correctly
- Not combining like terms correctly
- Not isolating the variable correctly
- Not checking the answer
Conclusion
Solving linear equations is a crucial skill for students to master, and with practice, you can become proficient in solving even the most complex equations. Remember to follow the order of operations, distribute coefficients correctly, combine like terms, isolate the variable, and check your answer. With these tips and tricks, you'll be solving linear equations like a pro in no time!
Practice Problems
Try solving the following linear equations using the steps outlined in this article:
References
About the Author
[Your Name] is a mathematics educator with a passion for helping students understand complex mathematical concepts. With years of experience in teaching and tutoring, [Your Name] has developed a unique approach to explaining mathematical concepts in a clear and concise manner.