Understanding the Equation: 6x + 20 = 120 Explained

Mathematics is all about solving problems using logical reasoning, and one of the simplest yet powerful ways to apply this is through solving linear equations. A common type many students encounter is equations in the form of 6x + 20 = 120. In this article, we’ll break down how to solve this equation step-by-step, understand its solution, and explore how mastering such problems enables better learning in algebra and beyond.

Understanding the Context

What is the Equation 6x + 20 = 120?

The expression 6x + 20 = 120 is a linear equation where:

  • 6x represents six times an unknown value x,
  • +20 is a constant added,
  • = 120 states that the entire left side equals 120.

Solving for x means finding the value that makes the equation true—universal in algebra and critical for building mathematical confidence.

6x + 20 = 120

Key Insights

Step-by-Step Solution to 6x + 20 = 120

Here’s how to isolate x:

  1. Start with the original equation:
    6x + 20 = 120

  2. Subtract 20 from both sides to eliminate the constant:
    6x + 20 – 20 = 120 – 20
    6x = 100

  3. Divide both sides by 6 to solve for x:
    6x ÷ 6 = 100 ÷ 6
    x = 100/6
    x = 50/3 (or approximately 16.67)

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Question: A science fiction writer designs a starship with 7 crew roles and 5 alien biome systems. How many ways can 3 crew roles and 2 biome systems be selected for a mission if each system requires a unique role?
Solution: First, choose 3 crew roles from 7: $\dbinom{7}{3}$. Then, select 2 biome systems from 5: $\dbinom{5}{2}$. Since each system needs a unique role, multiply by the number of ways to assign roles to biomes: $\dbinom{7}{3} \times \dbinom{5}{2} \times 3! = 35 \times 10 \times 6 = 2100$. However, if roles are independent of biomes, the answer simplifies to $\dbinom{7}{3} \times \dbinom{5}{2} = 35 \times 10 = 350$. Clarifying the problem's constraints, the most logical interpretation is $\boxed{350}$.
Question: A bioinformatics developer creates a tool to analyze 6 gene sequences and 4 protein markers. How many ways can 2 sequences and 2 markers be selected if one specific marker is mandatory for all selections?

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Final Thoughts

Why This Equation Matters: Real-World Applications

Understanding equations like 6x + 20 = 120 isn’t just theoretical. Here are a few ways they apply:

  • Budgeting & Finance: Imagine buying 6 items at $x each, spending a $20 fee, totaling $120. Solving gives x, your unit cost.
  • Time & Distance: If traveling at 6 miles per hour plus a 20-minute delay, covering 120 miles total, x helps calculate actual driving time.
  • Science & Engineering: Simplifying complex formulas often begins with linear equations like this one.

Tips for Solving Linear Equations Like This

  1. Isolate the variable term first by undoing constants.
  2. Use inverse operations—addition vs. subtraction, multiplication vs. division.
  3. Always check your solution by plugging x back into the original equation:
    6*(50/3) + 20 = 100 + 20 = 120 ✅
  4. Practice regularly—familiarity builds speed and accuracy.

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