43.) [tex]$10 x+36-38 x-47$[/tex]
Answer (2)
The expression 10 x + 36 − 38 x − 47 simplifies to − 28 x − 11 by combining like terms. The x terms combine to − 28 x and the constants combine to − 11 . Thus, the final simplified expression is − 28 x − 11 .
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Combine the 'x' terms: 10 x − 38 x = − 28 x .
Combine the constant terms: 36 − 47 = − 11 .
Combine the simplified terms: − 28 x − 11 .
The simplified expression is − 28 x − 11 .
Explanation
Understanding the Problem We are given the expression 10 x + 36 − 38 x − 47 and our goal is to simplify it by combining like terms. This involves grouping the terms with 'x' and the constant terms separately.
Combining 'x' Terms First, let's group the terms containing 'x': 10 x − 38 x . We can factor out the 'x' to get ( 10 − 38 ) x . Now, we perform the subtraction: 10 − 38 = − 28 . So, the simplified 'x' term is − 28 x .
Combining Constant Terms Next, let's group the constant terms: 36 − 47 . Performing the subtraction, we get 36 − 47 = − 11 .
Final Simplified Expression Finally, we combine the simplified 'x' term and the simplified constant term to get the fully simplified expression: − 28 x − 11 .
Conclusion Therefore, the simplified form of the given expression 10 x + 36 − 38 x − 47 is − 28 x − 11 .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics with numerous real-world applications. For example, imagine you are managing a budget where 'x' represents the number of hours you work. Your income might be represented as 10 x + 36 , where $10 is your hourly wage and $36 is a fixed bonus. Your expenses could be 38 x + 47 , where $38 is the cost per hour of some activity and $47 is fixed monthly expenses. Simplifying the expression 10 x + 36 − 38 x − 47 to − 28 x − 11 allows you to quickly determine your net income (or loss) based on the number of hours you work. If you work 5 hours ( x = 5 ), your net income would be − 28 ( 5 ) − 11 = − 140 − 11 = − $151 , indicating a loss. This kind of simplification helps in making quick financial assessments.
