As a professional teacher, one of the most important concepts I teach my students is how to solve equations for a variable. In this article, we will be exploring how to solve for x in the equation 2(5x+2)=48. We will break down the problem, explain the steps to solve it, and offer some tips to help you solve similar equations in the future.
Breaking Down the Equation
Let's start by breaking down the equation 2(5x+2)=48. This equation contains one variable, x, which we need to solve for. To solve for x, we need to isolate it on one side of the equation. To do this, we need to simplify the equation by using the order of operations. The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The acronym PEMDAS can help you remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Step 1: Simplify the Expression Inside the Parentheses
The first step in solving the equation is to simplify the expression inside the parentheses. We can do this by multiplying 5 and x, which gives us 5x. Then, we add 2 to 5x, which gives us 5x+2. Now, we can substitute 5x+2 back into the original equation: 2(5x+2)=48.
Step 2: Distribute the 2
The next step is to distribute the 2 to 5x+2. To do this, we multiply 2 by both 5x and 2, which gives us 10x+4. Our equation now looks like this: 10x+4=48.
Step 3: Simplify the Expression
The next step is to simplify the expression by subtracting 4 from both sides of the equation. This gives us 10x=44.
Step 4: Solve for X
Finally, we can solve for x by dividing both sides of the equation by 10. This gives us x=4.4.
Tips for Solving Equations
Now that we have solved the equation, let's discuss some tips that can help you solve similar equations in the future. 1. Follow the order of operations: Always remember to follow the order of operations when simplifying equations. This will help you avoid mistakes and ensure that you arrive at the correct answer. 2. Isolate the variable: To solve for a variable, you need to isolate it on one side of the equation. This means that you need to move all the other terms to the other side of the equation. 3. Check your answer: Always check your answer by substituting it back into the original equation. This will help you verify that your answer is correct.
Conclusion
In conclusion, solving equations for a variable is an important skill that every student should learn. By breaking down the problem and following the order of operations, you can solve equations like 2(5x+2)=48 with ease. Remember to isolate the variable and check your answer to ensure that you arrive at the correct solution. With practice, you can become proficient in solving equations and tackle more complex problems in the future.
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