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.

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.

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:

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.

Practice: Solve This Similar Equation

Want to try your hand?
Try solving:
4x - 3x + 8 = 13

Steps:

1. Combine 4x - 3x = x → x + 8 = 13
   
2. Subtract 8 from both sides → x = 5

Why Learning to Solve Linear Equations Matters

Understanding how to solve equations like 3x - 2x - 5 = 7 is essential for:

• Building foundation in algebra
  
• Preparing for advanced math topics such as systems of equations and graphing
  
• Developing logical thinking and analytical skills
  
• Success in STEM fields, economics, and everyday decision-making (budgeting, ratios, etc.)

Pro Tips for Solving Linear Equations

• Combine like terms first to simplify the expression.
  
• Perform the same operation on both sides to maintain equation balance.
  
• Use the inverse operations method: addition/subtraction for constants, multiplication/division for coefficients.
  
• Always verify your solution by substituting back into the original equation.
  
• Practice regularly with varied problems to build speed and confidence.

Summary

Solving 3x - 2x - 5 = 7 follows these simple steps: simplify (x - 5 = 7), then isolate x by adding 5, giving x = 12. With clear steps and verification, algebra becomes a powerful tool—no calculator required.

Whether you’re studying for a test, teaching a child, or just excited to decode equations, mastering 3x - 2x - 5 = 7 strengthens your mathematical foundation and empowers you to tackle more complex challenges.

Try it now: What is x in the equation 3x - 2x - 5 = 7?
Kick-start your algebra journey and unlock the power of equations!

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