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.

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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Final Thoughts

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.