3a - 5 = 8 - 2a - Coaching Toolbox
Solving 3a – 5 = 8 – 2a: A Step-by-Step Guide
Solving 3a – 5 = 8 – 2a: A Step-by-Step Guide
Solving linear equations can seem daunting at first, but with a structured approach, it becomes straightforward. One common problem students encounter is solving equations like 3a – 5 = 8 – 2a. Whether you're a high school student, a homeschooler, or just learning algebra, mastering this type of equation is essential. In this article, we’ll walk through how to solve 3a – 5 = 8 – 2a step by step, explain key algebraic concepts, and provide tips to build confidence in solving similar problems.
Understanding the Context
Understanding the Equation: What Does 3a – 5 = 8 – 2a Mean?
The equation 3a – 5 = 8 – 2a contains an unknown variable a on both sides—and different coefficients (3 and –2) and constants (5 and 8). This type of equation is called a linear equation in one variable, where the variable appears only once to the first power.
Our goal is to isolate a to determine its value. This requires applying algebraic operations to both sides while maintaining equality.
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Key Insights
Step-by-Step Solution to 3a – 5 = 8 – 2a
Step 1: Eliminate parentheses and combine like terms
The equation has no parentheses, but we can isolate a by gathering all terms containing the variable on one side and constants on the other.
Start with:
3a – 5 = 8 – 2a
Add 2a to both sides to bring all a terms together:
3a + 2a – 5 = 8
5a – 5 = 8
Now the variable a is on the left, and constants/day coefficients are on the right.
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Step 2: Isolate the constant terms
Subtract 5 from both sides to eliminate the constant on the left:
5a – 5 – 5 = 8 – 5
5a = 3
Step 3: Solve for a
Now divide both sides by 5 to isolate a:
a = 3 ÷ 5
a = 0.6
Final Answer
✅ The solution to the equation 3a – 5 = 8 – 2a is a = 0.6 (or a = 3/5 in fraction form).
Key Takeaways from Solving 3a – 5 = 8 – 2a
1. Balance is Key
Every operation you perform—adding, subtracting, multiplying—must be applied to both sides. This preserves the equation’s equality.
