Combined: $ x + (4x + 6) = 102 $. - Coaching Toolbox
Title: Solve the Equation: Combined x + (4x + 6) = 102 – Step-by-Step Guide
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.
Understanding the Context
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.
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Key Insights
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.
$$
x + 4x + 6 = 102
$$
$$
(1x + 4x) + 6 = 102
$$
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$$
5x + 6 = 102
$$
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:
$$
x = rac{96}{5}
$$
