2x + 3(4x - 9) = 16 - Dachbleche24

How to Solve 2x + 3(4x - 9) = 16: Step-by-Step Guide with Problem-Solving Tips

Mathematics often presents challenges, but solving equations like 2x + 3(4x - 9) = 16 doesn’t have to be tricky. Whether you're a student studying algebra, preparing for a math test, or simply looking to sharpen your equation-solving skills, this guide walks you through the process using a clear, structured method. Mastering this skill helps build problem-solving confidence and lays a strong foundation for algebra and beyond.

Understanding the Context

What Is the Equation?

We begin with the linear equation:
2x + 3(4x - 9) = 16

This equation combines a simple linear term (2x) with a distributed term (3 times a binomial). Solving it involves distributing, combining like terms, and isolating the variable — all key skills in algebra.

Key Insights

Step 1: Distribute the 3 Across the Parentheses

The first move is to eliminate the parentheses by distributing the 3:
3 × 4x = 12x
3 × (−9) = −27

So the equation becomes:
2x + 12x - 27 = 16

Step 2: Combine Like Terms

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Final Thoughts

Now combine the x-terms on the left-hand side:
2x + 12x = 14x

Now the equation is:
14x - 27 = 16

Step 3: Isolate the Variable Term

Add 27 to both sides to move the constant to the right:
14x − 27 + 27 = 16 + 27
14x = 43

Step 4: Solve for x

Divide both sides by 14:
x = 43 ÷ 14
x = 43/14 (in simplest form)

You can also express it as a decimal: x ≈ 3.07 (rounded to two decimal places).