2x + 12x - 27 = 16
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 Equation
Start by simplifying the left-hand side of the equation:
2x + 12x - 27 = 16
Combine like terms:
- 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
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)
Final Answer
The solution to the equation 2x + 12x - 27 = 16 is:
x = 43/14 or x ≈ 3.07
Why Solving Linear Equations Matters
Solving equations like 2x + 12x - 27 = 16 helps build foundational algebra skills used in STEM fields, finance, engineering, and everyday problem solving. Mastering these steps improves logical reasoning and analytical thinking.
Summary of Steps
- Combine like terms: 2x + 12x → 14x
- Add 27 to both sides: 14x = 43
- Divide by 14 to isolate x: x = 43/14
Feel free to practice with similar equations like 5x + 3x - 10 = 26 to strengthen your algebra skills!
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