Six Less Than Twice A Number X Is 38

Understanding the Equation: Six Less Than Twice a Number x is 38

Algebra is a fundamental branch of mathematics that allows us to solve problems using variables and equations. Consider this: one common type of algebraic problem involves translating word problems into mathematical expressions. But a classic example is the phrase "six less than twice a number x is 38. " This statement may seem simple at first glance, but it contains important clues about how to set up and solve the equation.

Breaking Down the Problem

To solve this problem, we need to carefully interpret each part of the phrase. The key words here are "six less than," "twice," and "is." Each of these terms has a specific mathematical meaning:

• "Twice a number x" means we multiply x by 2, giving us 2x.
• "Six less than" indicates subtraction, meaning we subtract 6 from the previous result.
• "Is" translates to an equals sign (=) in an equation.

Putting it all together, the phrase "six less than twice a number x is 38" becomes the equation:

2x - 6 = 38

Solving the Equation

Now that we have our equation, the next step is to solve for x. Here's how we do it:

1. Add 6 to both sides of the equation to isolate the term with x:

   2x - 6 + 6 = 38 + 6 2x = 44

2. Divide both sides by 2 to solve for x:

   2x / 2 = 44 / 2 x = 22

So, the number x is 22.

Checking the Solution

It's always a good idea to verify our solution by plugging it back into the original equation:

2x - 6 = 38 2(22) - 6 = 38 44 - 6 = 38 38 = 38

Since both sides are equal, we have confirmed that x = 22 is the correct solution.

Why This Problem Matters

Understanding how to translate and solve word problems like this is crucial for developing strong algebra skills. These types of problems appear frequently in math classes, standardized tests, and real-world applications. They teach us how to think logically, break down complex statements, and use mathematical operations to find unknown values.

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Worth adding, mastering these skills builds a foundation for more advanced topics in algebra, such as solving systems of equations, working with inequalities, and even calculus.

Common Mistakes to Avoid

When solving equations like "six less than twice a number x is 38," students often make a few common errors:

• Misinterpreting "less than": Remember, "six less than" means you subtract 6 after performing the multiplication. It does not mean 6 - 2x.
• Forgetting to perform the same operation on both sides: When solving equations, whatever you do to one side, you must do to the other to keep the equation balanced.
• Skipping the check step: Always verify your solution by substituting it back into the original equation.

Practice Problems

To reinforce your understanding, try solving these similar problems:

1. Seven more than three times a number y is 28. What is y?
2. Four less than five times a number z is 31. What is z?
3. Nine less than twice a number w is 15. What is w?

Conclusion

The problem "six less than twice a number x is 38" is a classic example of how algebra allows us to solve for unknown values using logical steps. Even so, by translating the words into an equation, solving for x, and checking our work, we find that x = 22. So this process not only helps us solve this particular problem but also strengthens our overall mathematical reasoning and problem-solving skills. With practice, you'll become more confident in tackling a wide variety of algebraic word problems.

Conclusion

To keep it short, solving algebraic equations, especially those presented as word problems, is a fundamental skill in mathematics. By understanding the underlying principles and avoiding common pitfalls, students can confidently tackle a wide range of algebraic challenges. The ability to apply these skills not only provides a solid foundation for future mathematical studies but also cultivates valuable problem-solving abilities applicable across various disciplines. The process involves translating the word problem into a mathematical equation, isolating the variable, and verifying the solution. Consistent practice with different types of problems will undoubtedly lead to greater proficiency and a deeper understanding of the power of algebra.