How to Solve the Equation: x + 2x + (2x – 10,000) = 240,000 Step-by-Step

Understanding algebra is essential for solving real-world problems, and breaking down equations step-by-step is key to finding accurate solutions. In this article, we’ll solve the equation:

x + 2x + (2x – 10,000) = 240,000

Understanding the Context

— a common type of equation found in finance, budgeting, and data analysis. Knowing how to solve it not only improves your math skills but also helps in solving practical challenges like calculating investments, savings, or break-even points.

Step 1: Combine Like Terms

Start by combining all the x terms on the left side:

Total: x + 2x + (2x – 10,000) = 240,000 → 5x – 10,000 = 240,000 → 5x = 250,000 → x = <<250000/5=50000>>50,000

Key Insights

  • x + 2x + 2x = 5x

So the equation becomes:

5x – 10,000 = 240,000

Step 2: Isolate the Variable Term

Continue Reading

If the function \( f(x) = 2x^2 - 4x - 6 \) has a root at \( x = 3 \), find the other root.
Use the fact that the sum of the roots of \( ax^2 + bx + c = 0 \) is \(-\frac{b}{a}\). Here, \( a = 2 \), \( b = -4 \):
\text{Sum of roots} = -\left(-\frac{-4}{2}\right) = 2

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Final Thoughts

Add 10,000 to both sides to eliminate the constant on the left:

5x = 240,000 + 10,000
5x = 250,000

Step 3: Solve for x

Now divide both sides by 5:

x = 250,000 ÷ 5
x = 50,000

Final Answer

x = 50,000