Solve the Linear Equation: 7x + 4x + 5x = 0

Q: Why do I only add the numbers in front of x?

The numbers (7, 4, 5) are called coefficients. When you have like terms (all containing x), you add the coefficients and keep the variable part unchanged. Think of it like: 7 apples + 4 apples + 5 apples = 16 apples.

Q: What if the equation was 16x = 8 instead of 16x = 0?

Then you'd divide both sides by 16 to get $ x = \frac{8}{16} = \frac{1}{2} $. But since we have 16x = 0, dividing by 16 gives us x = 0.

Q: Can x equal zero in math problems?

Absolutely! Zero is a perfectly valid answer. Many equations have x = 0 as their solution. Don't second-guess yourself just because the answer seems 'too simple'.

Q: What's the difference between 16x and 16 × x?

They mean exactly the same thing! 16x is just the shortened way to write 16 × x. In algebra, we skip the multiplication symbol when a number is next to a variable.

Linear Equations with Like Terms

$7x+4x+5x=0$

$x=\text{?}$

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, we need to find the value of X.

00:09 Next, let's gather all the factors together.

00:13 Now, we'll isolate X by moving other terms away.

00:20 Then, reduce everything as much as you can.

00:25 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$7x+4x+5x=0$

$x=\text{?}$

Step-by-step solution

Let's combine all the x terms together:

$7x+4x+5x=11x+5x=16x$

The resulting equation is:

$16x=0$

Now let's divide both sides by 16:

$\frac{16x}{16}=\frac{0}{16}$

$x=\frac{0}{16}=0$

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Combining Like Terms: Add coefficients of x terms: 7x + 4x + 5x = 16x
Technique: Simplify 7 + 4 + 5 = 16, so 16x = 0
Check: Substitute x = 0: 7(0) + 4(0) + 5(0) = 0 + 0 + 0 = 0 ✓

Common Mistakes

Avoid these frequent errors

Adding x variables incorrectly
Don't write 7x + 4x + 5x = 16x³ or 16x² = wrong operations! This treats x as a factor to multiply instead of a variable with coefficients. Always add only the coefficients: 7 + 4 + 5 = 16, keeping x as 16x.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I only add the numbers in front of x?

The numbers (7, 4, 5) are called coefficients. When you have like terms (all containing x), you add the coefficients and keep the variable part unchanged. Think of it like: 7 apples + 4 apples + 5 apples = 16 apples.

What if the equation was 16x = 8 instead of 16x = 0?

Then you'd divide both sides by 16 to get $x = \frac{8}{16} = \frac{1}{2}$ . But since we have 16x = 0, dividing by 16 gives us x = 0.

Can x equal zero in math problems?

Absolutely! Zero is a perfectly valid answer. Many equations have x = 0 as their solution. Don't second-guess yourself just because the answer seems 'too simple'.

How do I combine terms when some have negative signs?

Treat negative signs as part of the coefficient. For example: 3x - 2x + 5x becomes (3 - 2 + 5)x = 6x. Just be careful with the signs when adding!

What's the difference between 16x and 16 × x?

They mean exactly the same thing! 16x is just the shortened way to write 16 × x. In algebra, we skip the multiplication symbol when a number is next to a variable.

🌟 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