3x + 2(10 - x) = 24 \Rightarrow 3x + 20 - 2x = 24 \Rightarrow x + 20 = 24 \Rightarrow x = 4 - Silent Sales Machine
Solving the Linear Equation: 3x + 2(10 − x) = 24
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
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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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.
