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.

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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Final Thoughts

$$
5x + 6 = 102
$$

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:

$$
x = rac{96}{5}
$$