How to Solve the Equation 2x + 12x - 27 = 16 | Step-by-Step Guide

Solving linear equations like 2x + 12x - 27 = 16 is essential for mastering algebra. Whether you're a student, teacher, or home learner, understanding how to isolate the variable step-by-step empowers you to tackle similar math problems with confidence. In this article, we break down the process for solving 2x + 12x - 27 = 16, explaining each step clearly for better comprehension.

Understanding the Context

Understanding the Equation

Start by simplifying the left-hand side of the equation:

2x + 12x - 27 = 16

Combine like terms:

2x + 12x - 27 = 16

Key Insights

  • The terms 2x and 12x are like terms since both contain x.
  • Add them:
     2x + 12x = 14x

So the equation becomes:

14x - 27 = 16

Step 1: Isolate the Variable Term

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Final Thoughts

To isolate 14x, add 27 to both sides of the equation to eliminate the constant term on the left:

14x - 27 + 27 = 16 + 27

Simplify:
14x = 43

Step 2: Solve for x

Now divide both sides by 14 to solve for x:

x = 43 ÷ 14

So:

x = 43/14 (this is an exact fraction)
or approximately x ≈ 3.07 (decimal form)