Solve for x: 25x - 10x = 5000 – A Step-by-Step Breakdown

Understanding how to solve basic algebraic equations is essential for mastering algebra and tackling more complex math problems. One common equation students frequently encounter is:

25x - 10x = 5000

Understanding the Context

Beyond just writing the solution, it’s important to follow through the steps logically to build confidence and ensure accuracy. Let’s break down the process of solving this equation step by step.

Step 1: Simplify the Left-Hand Side

Start with the original equation:
25x - 10x = 5000

Solve for x: 25x - 10x = 5000, 15x = 5000, x = 5000 / 15, x = 333.33.

Key Insights

Combine like terms on the left side by subtracting:
25x – 10x = 15x

Now the equation becomes:
15x = 5000

Step 2: Isolate x

To solve for x, divide both sides of the equation by 15:
x = 5000 ÷ 15

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Final Thoughts

Step 3: Calculate the Value

Perform the division:
5000 ÷ 15 = 333.33 (rounded to two decimal places)

So, the solution is:
x = 333.33

Why This Matters

Equations like 25x - 10x = 5000 appear in real-life scenarios involving linear relationships—from budgeting and finance to physics and engineering. Learning to solve for x provides a foundational skill critical for problem-solving in any STEM field.

Final Answer

x = 333.33
(Alternatively written as x ≈ 333.33 or 333 ⁔)