Combined: $ x + (4x + 6) = 102 $.
Title: Solve the Equation: Combined x + (4x + 6) = 102 – Step-by-Step Guide
Meta Description: Learn how to solve the algebra equation Combined x + (4x + 6) = 102 easily. Step-by-step solution with clear explanations for students and math learners.
Combined Equation: Solve for $ x $ in $ x + (4x + 6) = 102 $
Understanding how to combine and solve algebraic equations is essential for solving real-world problems. One common equation students frequently encounter is:
$$ x + (4x + 6) = 102 $$
In this article, we’ll break down how to correctly interpret, simplify, and solve this equation step-by-step — also explaining key concepts to strengthen your algebra skills.
Step 1: Combine Like Terms
The expression $ x + (4x + 6) $ contains two parts: a linear term $ x $ and a binomial $ 4x + 6 $. To simplify, combine like terms — that is, the $ x $ terms with other $ x $ terms.
$$ x + 4x + 6 = 102 $$
$$ (1x + 4x) + 6 = 102 $$
$$ 5x + 6 = 102 $$
Step 2: Isolate the Variable Term
Now that we have simplified the left-hand side, we aim to isolate $ x $. Start by subtracting 6 from both sides:
$$ 5x + 6 - 6 = 102 - 6 $$
$$ 5x = 96 $$
Step 3: Solve for $ x $
To find $ x $, divide both sides by 5:
$$ x = rac{96}{5} $$
$$ x = 19.2 $$
Final Answer
$$ x = 19.2 $$
Why Understanding This Matters
The equation $ x + (4x + 6) = 102 $ is a foundational algebra problem used in physics, engineering, economics, and computer science to model relationships and solve unknowns. Mastering combination of terms and equation balancing builds confidence and precision in higher-level math.
Bonus Tips for Solving Similar Equations
- Always simplify inside parentheses first.
- Combine like terms (like $ x + 4x = 5x $) before solving.
- Isolate variables by performing inverse operations on both sides.
- Check your solution by substituting $ x $ back into the original equation.
Ready to apply this skill? Try solving these variations:
- $ 3x + (2x + 8) = 70 $
- $ 5x - (x - 4) = 16 $
Practice makes perfect — and understanding equations like $ x + (4x + 6) = 102 $ is your first step to algebra mastery!
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