3z - 8z = 2 + 5 - Coaching Toolbox
Solving 3z – 8z = 2 + 5: A Step-by-Step Guide to Solve Linear Equations
Solving 3z – 8z = 2 + 5: A Step-by-Step Guide to Solve Linear Equations
Mathematics often presents challenges in the form of equations that demand step-by-step logic to unlock their solutions. One such equation that many students encounter is 3z – 8z = 2 + 5. While it might seem simple at first glance, understanding how to solve it properly not only helps with algebra basics but builds a strong foundation for more complex problem-solving.
In this article, we’ll break down how to solve 3z – 8z = 2 + 5, explain the important algebraic steps, and highlight why mastering such equations is key in both school and real-world applications.
Understanding the Context
What Is the Equation: 3z – 8z = 2 + 5?
At first glance, this is a linear equation involving one variable, z. Though the expression looks short, correctly simplifying and solving it requires attention to order of operations and basic algebraic principles.
Let’s rewrite it clearly:
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Key Insights
3z – 8z = 2 + 5
Step 1: Simplify Both Sides
Start by simplifying both sides using arithmetic rules:
- Left side: 3z – 8z = -5z
- Right side: 2 + 5 = 7
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Now the equation becomes:
-5z = 7
Step 2: Isolate the Variable z
To solve for z, divide both sides by –5:
z = 7 ÷ (–5)
z = –7/5
This fraction can also be written as the decimal –1.4, offering two common ways to express the solution.
Why Is Solving Such Equations Important?
Solving linear equations like 3z – 8z = 2 + 5 is fundamental not only in algebra but in many practical scenarios:
