How to Solve 3x - 2x - 5 = 7: Step-by-Step Guide with Free Math Tips

Solving simple linear equations like 3x - 2x - 5 = 7 is a fundamental skill in algebra that helps build problem-solving confidence. Whether you're a student, teacher, or someone brushing up on math basics, this article walks you through solving the equation step by step, explains the logic behind each action, and provides practical tips to master similar problems.

Understanding the Context

Step 1: Understand the Equation

Begin by analyzing the equation:

3x - 2x - 5 = 7

This is a linear equation involving a single variable x. The goal is to isolate x on one side of the equation to find its value.

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Key Insights

Step 2: Combine Like Terms

Simplify the left-hand side by combining like terms.

On the left: 3x - 2x
Since both terms contain x, subtract:
3x - 2x = x

Now rewrite the equation:

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Final Thoughts

x - 5 = 7

Step 3: Isolate the Variable

To solve for x, eliminate the constant term on the left. Add 5 to both sides of the equation:

x - 5 + 5 = 7 + 5
x = 12

Step 4: Check the Solution

Plug x = 12 back into the original equation to verify:

3(12) - 2(12) - 5 = 7
36 - 24 - 5 = 7
7 = 7 ✅

The solution checks and confirms x = 12 is correct.