Frage: Der Durchschnitt von $ 3x+2 $, $ 5x-4 $, und $ 4x+7 $ ist $ 10 $. Was ist der Wert von $ x $?

Mon, 20 Apr 2026 04:15:01 +0000

**How $ 3x+2 $, $ 5x-4 $, and $ 4x+7 $ Average to 10—What Does It Really Mean?** Curious about how this algebraic question reflects real-world problem-solving? Many learners now explore equations like Frage: Der Durchschnitt von $ 3x+2 $, $ 5x-4 $, und $ 4x+7 $ ist $ 10 $. What is the value of $ x $? At first glance, it seems like a standard math puzzle—but beneath the numbers lies deeper insight into logic, averages, and real-life literacy in data. With economic shifts and growing interest in financial literacy, understanding how averages function helps people make clearer decisions in personal budgeting, investing, and trend analysis. This article uncovers the logic behind this common question—so you gain more than just an answer, but sustainable confidence in interpreting similar challenges. The average of multiple expressions begins by summing them, then dividing by the count. For expressions $ 3x+2 $, $ 5x-4 $, and $ 4x+7 $, adding yields:
$ (3x + 5x + 4x) + (2 - 4 + 7) = 12x + 5 $.
Dividing by 3 (since there are three terms) gives $ \frac{12x + 5}{3} $. Setting this equal to 10 forms the equation:
$ \frac{12x + 5}{3} = 10 $. Solving smoothly follows logic anyone can follow: multiply both sides by 3 to eliminate the denominator, resulting in $ 12x + 5 = 30 $. Subtracting 5 gives $ 12x = 25 $, then dividing by 12 yields $ x = \frac{25}{12} $, or approximately $ 2.083 $. This precise value reveals not just a number, but a clear path through arithmetic steps—something learners today value for clarity and accuracy.