Solve Linear Equation: Finding X in 3x - x = 8

Q: What does 'like terms' mean exactly?

Like terms are terms with the same variable raised to the same power. In $ 3x - x $, both terms have the variable x to the first power, so they're like terms!

Q: Why can't I just divide both sides by 3 right away?

Because you have two different terms on the left: 3x and -x. You must combine them first to get 2x, then divide by 2, not 3.

Q: How do I combine 3x - x step by step?

Think of it as: $ 3x - 1x = (3-1)x = 2x $. You're subtracting the coefficients (the numbers in front) and keeping the variable x.

Q: What if I had 3x + x instead?

Then you'd add the coefficients: $ 3x + 1x = (3+1)x = 4x $. The same rule applies - combine the numbers, keep the variable!

Q: How can I check if x = 4 is really correct?

Substitute 4 for x in the original equation: $ 3(4) - 4 = 12 - 4 = 8 $. Since this equals 8, your answer is correct!

Linear Equations with Like Terms

$3x - x = 8$

$x = \text{?}$

❤️ 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

$3x - x = 8$

$x = \text{?}$

Step-by-step solution

Start by simplifying the left-hand side of the equation:

$3x - x = 2x$

So the equation becomes:

$2x = 8$

To find the value of $x$ , divide both sides by 2:

$x = \frac{8}{2}$

Then simplify the fraction:

$x = 4$

Thus, the solution to the equation is $x = 4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Combining Like Terms: Subtract coefficients of same variables (3x - x = 2x)
Technique: Simplify left side first: 3x - x = 2x, then solve 2x = 8
Check: Substitute back: 3(4) - 4 = 12 - 4 = 8 ✓

Common Mistakes

Avoid these frequent errors

Trying to solve without combining like terms first
Don't jump straight to dividing by 3 or subtracting x from both sides = wrong answer! This skips the essential step of simplifying. Always combine like terms on each side before isolating the variable.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

What does 'like terms' mean exactly?

Like terms are terms with the same variable raised to the same power. In $3x - x$ , both terms have the variable x to the first power, so they're like terms!

Why can't I just divide both sides by 3 right away?

Because you have two different terms on the left: 3x and -x. You must combine them first to get 2x, then divide by 2, not 3.

How do I combine 3x - x step by step?

Think of it as: $3x - 1x = (3-1)x = 2x$ . You're subtracting the coefficients (the numbers in front) and keeping the variable x.

What if I had 3x + x instead?

Then you'd add the coefficients: $3x + 1x = (3+1)x = 4x$ . The same rule applies - combine the numbers, keep the variable!

How can I check if x = 4 is really correct?

Substitute 4 for x in the original equation: $3(4) - 4 = 12 - 4 = 8$ . Since this equals 8, your answer is correct!

🌟 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