How to Simplify the Equation: 3x + 6 = 90 – A Step-by-Step Guide

Solving math problems isn’t always easy, especially when equations look complicated at first glance. One basic but essential algebra equation that often trips students is 3x + 6 = 90. Whether you're a student learning intermediate algebra or someone brushing up on problem-solving skills, understanding how to simplify and solve this equation is key to building confidence in math.

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Understanding the Context

What is the Equation 3x + 6 = 90?

3x + 6 = 90 is a linear equation involving one variable, x. The goal is to find the value of x that makes the equation true. Such equations are foundational in algebra and widely used in real-world applications—from budgeting to science calculations.

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Key Insights

Step-by-Step Simplification & Solution

Simplifying the equation means transforming it into a form where x is isolated on one side. Here’s how:

Step 1: Subtract 6 from Both Sides

To isolate the term with x, eliminate constants first. Subtract 6 from both sides:

$$
3x + 6 - 6 = 90 - 6
$$
$$
3x = 84
$$

Step 2: Divide Both Sides by 3

Now divide both sides by 3 to solve for x:

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Final Thoughts

$$
rac{3x}{3} = rac{84}{3}
$$
$$
x = 28
$$

Final Answer

$$
x = 28
$$

To verify: plug 28 back into the original equation:
$$
3(28) + 6 = 84 + 6 = 90
$$
✅ The solution checks!

Why Simplifying Equations Matters

Understanding how to simplify and solve equations like 3x + 6 = 90 helps strengthen core math skills. Here are some benefits:

  • Builds algebra proficiency
  • Enhances problem-solving and logical reasoning
  • Prepares learners for advanced math topics
  • Boosts confidence in tackling real-world problems

Whether you're studying for exams, learning for personal enrichment, or teaching algebra, mastering equation simplification is invaluable.