Then: $ 3x - 24 = 96 $.
Solving $ 3x - 24 = 96 $: Step-by-Step Guide to Find the Value of x
If you're working on solving linear equations like $ 3x - 24 = 96 $, you're starting with a classic algebra principle that’s essential for students, teachers, and math learners. Understanding how to isolate the variable $ x $ unlocks the key to solving many real-world problems — from budgeting and calculating distances to understanding scientific models. In this SEO-optimized guide, we’ll walk you through solving the equation $ 3x - 24 = 96 $ step-by-step, improve your math skills, and boost your visibility on search engines by targeting high-value keywords.
Understanding the Equation $ 3x - 24 = 96 $
The equation $ 3x - 24 = 96 $ is a first-degree linear equation, where the variable $ x $ is multiplied by a coefficient (3), there is a constant term (-24), and the result equals 96. These equations are foundational in algebra and form the basis for more advanced math topics.
Why learn this equation?
- Mastery of linear equations improves problem-solving abilities.
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Step-by-Step Solution to $ 3x - 24 = 96 $
Step 1: Isolate the term with $ x $
To begin solving for $ x $, eliminate the constant on the left side. Add 24 to both sides:
$$ 3x - 24 + 24 = 96 + 24 $$
Simplify:
$$ 3x = 120 $$
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Step 2: Solve for $ x $ by dividing both sides by 3
Now that $ 3x = 120 $, divide both sides by 3 to isolate $ x $:
$$ rac{3x}{3} = rac{120}{3} $$
Simplify:
$$ x = 40 $$
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Final Answer
$$ oxed{x = 40} $$
This means that when $ x = 40 $, the original equation is satisfied:
$$ 3(40) - 24 = 120 - 24 = 96 $$
Why This Equation Matters – Real-World Applications
Equations like $ 3x - 24 = 96 $ model real-life situations such as:
- Budgeting: Calculating how many items you can buy given a fixed amount, after subtracting expenses.
- Distance and Speed: Finding time or speed in motion problems where distance depends linearly on time.
- Science: Relating variables in physics formulas (e.g., motion scenarios or chemical balance).
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Practice Problems to Boost Your Skills
- Solve $ 4x + 12 = 40 $
- Find $ x $ if $ 5x - 30 = 75 $
- What is $ x $ in $ 2x + 7 = 23 $?
Mastering these continues your journey from basic linear equations to more complex algebraic expressions.
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Conclusion
Solving $ 3x - 24 = 96 $ may seem simple — but it’s the foundation of algebraic thinking. With step-by-step clarity and strategic SEO, you've learned not just the answer, but how to apply this method everywhere math meets practical life. Keep practicing, and soon these techniques will become second nature.
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