Solving the Linear Equation: 3x + 2(10 − x) = 24

Understanding how to solve linear equations is a fundamental skill in algebra—essential not only for academics but also for real-world problem-solving. In this comprehensive guide, we will walk step-by-step through the solution of the equation:
3x + 2(10 − x) = 24

The Original Equation

Start with the equation:
3x + 2(10 − x) = 24

Understanding the Context

Step 1: Expand the Parentheses

The first step is to eliminate the parentheses. Multiply 2 across the terms inside:
3x + 2 × 10 − 2 × x = 24
Which simplifies to:
3x + 20 − 2x = 24

Step 2: Combine Like Terms

Combine the x-terms on the left side:
(3x − 2x) + 20 = 24
This gives:
x + 20 = 24

Step 3: Isolate the Variable

Subtract 20 from both sides to solve for x:
x + 20 − 20 = 24 − 20
Therefore:
x = 4

Final Answer

The solution to the equation 3x + 2(10 − x) = 24 is:
x = 4

$3x + 2(10 - x) = 24 \Rightarrow 3x + 20 - 2x = 24 \Rightarrow x + 20 = 24 \Rightarrow x = 4$

Key Insights

Why This Matters: Real-World Applications

Linear equations model everyday scenarios such as budgeting, mixing solutions, or comparing costs. Mastering their solution helps build logical reasoning and analytical thinking—skills useful in science, engineering, economics, and more.

Alternative Problem: Why 3x + 2(10 − x) = 24 Matters

This particular equation forces us to simplify and combine like terms, a common step in more complex algebraic manipulation. Practicing this helps students recognize patterns and improve speed and accuracy.

Practice Problems to Master

Try solving these equations like the example above:
- 5x + 3(8 − x) = 27
- 2(4 + x) − 3x = 10
- 4(x − 1) + 5x = 25–₴

Summary

Solving 3x + 2(10 − x) = 24 follows standard algebraic steps: expand, combine like terms, isolate x. The clear process demonstrates how simplification unlocks the solution. Whether for homework or future challenges, proficiency in linear equations opens doors to deeper mathematical mastery.

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Final Thoughts

Keywords: linear equations, solving equations, algebra, 3x + 2(10 − x) = 24, step-by-step solution, algebra tutorial, x = 4, math practice, solving equations with parentheses, algebra basics

Meta Description: Learn how to solve 3x + 2(10 − x) = 24 step-by-step. Discover the solution x = 4, review key algebra techniques, and practice similar equations for better math skills.