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Understanding the Equation: 6x + 20 = 120 Explained
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.
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Key Insights
Step-by-Step Solution to 6x + 20 = 120
Here’s how to isolate x:
-
Start with the original equation:
6x + 20 = 120 -
Subtract 20 from both sides to eliminate the constant:
6x + 20 – 20 = 120 – 20
6x = 100 -
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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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
- Isolate the variable term first by undoing constants.
- Use inverse operations—addition vs. subtraction, multiplication vs. division.
- Always check your solution by plugging x back into the original equation:
6*(50/3) + 20 = 100 + 20 = 120 ✅ - Practice regularly—familiarity builds speed and accuracy.
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