Solve for X in the Linear Equation: 6x-3=7x+5

Q: Why do I subtract 6x instead of 7x from both sides?

You can subtract either one! The goal is to get all x terms on one side. Subtracting 6x gives you $ -3 = x + 5 $, while subtracting 7x gives you $ -x - 3 = 5 $. Both work!

Q: What if I get confused about which direction to move terms?

Remember: when you move a term across the equals sign, it changes sign. So $ 6x - 3 = 7x + 5 $ becomes $ -3 - 5 = 7x - 6x $ when you move everything.

Q: Can I check my answer a different way?

Yes! Try graphing both sides as separate functions: $ y = 6x - 3 $ and $ y = 7x + 5 $. They should intersect at the point (-8, -51).

Q: What if I make an arithmetic mistake?

Always double-check your arithmetic! For example, $ -3 - 5 = -8 $, not +2. When you're subtracting a positive number, you're adding a negative: -3 + (-5) = -8.

Linear Equations with Variable Terms on Both Sides

Solve for X:

$6x-3=7x+5$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$6x-3=7x+5$

Step-by-step solution

The given equation is: $6x-3=7x+5$

Our goal is to solve for $x$ . To achieve this, we'll first get all the terms containing $x$ on one side of the equation and constants on the other side.

Step 1: Subtract $6x$ from both sides to get all $x$ terms on one side:

$6x - 3 - 6x = 7x + 5 - 6x$

This simplifies to:

$-3 = x + 5$

Step 2: Next, subtract $5$ from both sides to isolate $x$ :

$-3 - 5 = x + 5 - 5$

This simplifies to:

$-8 = x$

Therefore, the solution for $x$ is $-8$ .

Final Answer

$-8$

Key Points to Remember

Essential concepts to master this topic

Strategy: Move all variable terms to one side, constants to the other
Technique: Subtract 6x from both sides to get -3 = x + 5
Check: Substitute x = -8: 6(-8) - 3 = -51 and 7(-8) + 5 = -51 ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting incorrectly when moving terms
Don't subtract 6x from only one side and get 6x - 3 = x + 5! This breaks the equation's balance and gives wrong answers. Always perform the same operation to both sides of the equation.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

Why do I subtract 6x instead of 7x from both sides?

You can subtract either one! The goal is to get all x terms on one side. Subtracting 6x gives you $-3 = x + 5$ , while subtracting 7x gives you $-x - 3 = 5$ . Both work!

What if I get confused about which direction to move terms?

Remember: when you move a term across the equals sign, it changes sign. So $6x - 3 = 7x + 5$ becomes $-3 - 5 = 7x - 6x$ when you move everything.

How do I know my final answer is negative?

Don't worry about the sign until the end! Follow the algebra steps carefully: $-3 - 5 = -8$ . A negative answer is completely normal in algebra.

Can I check my answer a different way?

Yes! Try graphing both sides as separate functions: $y = 6x - 3$ and $y = 7x + 5$ . They should intersect at the point (-8, -51).

What if I make an arithmetic mistake?

Always double-check your arithmetic! For example, $-3 - 5 = -8$ , not +2. When you're subtracting a positive number, you're adding a negative: -3 + (-5) = -8.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime