Solve the Linear Equation: x + 8 + 3x - 4 = 0

Q: What are 'like terms' exactly?

Like terms have the same variable part. In this equation, $ x $ and $ 3x $ are like terms because they both have x. The constants 8 and -4 are also like terms because they have no variables.

Q: Why do I combine like terms first?

Combining like terms simplifies the equation and makes it easier to solve. Instead of working with 4 separate terms, you get just 2 terms: $ 4x + 4 = 0 $.

Q: How do I handle the negative sign in front of 4?

The equation is $ x + 8 + 3x - 4 $, so you're adding 8 and subtracting 4. Think of it as $ 8 + (-4) = 4 $.

Q: What if I get a different answer?

Double-check your sign tracking and combining steps! The most common errors happen when combining constants or coefficients. Remember: $ x + 3x = 4x $ (not 3x) and $ 8 - 4 = 4 $ (not 12).

Q: Can I solve this equation in a different order?

Yes! You could move terms to different sides first, but combining like terms first is usually easier and less error-prone. It keeps your work organized and clear.

Linear Equations with Like Terms Combining

$x+8+3x-4=0$

$x=\text{?}$

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Step-by-step video solution

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00:05 Let's find the value of X!

00:09 First, we need to collect all like terms.

00:13 Next, arrange the equation so that X is on one side by itself.

00:20 Now, let's isolate X to see its value.

00:30 And there you have it! That's how we find X.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$x+8+3x-4=0$

$x=\text{?}$

Step-by-step solution

To solve the linear equation $x + 8 + 3x - 4 = 0$ , follow these steps:

Step 1: Combine like terms.
Combine the terms involving $x$ , specifically $x + 3x = 4x$ .
Combine the constant terms, specifically $8 - 4 = 4$ .
The equation becomes $4x + 4 = 0$ .
Step 2: Isolate the variable $x$ .
Subtract 4 from both sides to get $4x = -4$ .
Step 3: Solve for $x$ .
Divide both sides by 4 to solve for $x$ , resulting in $x = -1$ .

Therefore, the solution to the equation is $x = -1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Combining Rule: Group x terms together and constant terms together
Technique: $x + 3x = 4x$ and $8 - 4 = 4$
Check: Substitute $x = -1$ : $(-1) + 8 + 3(-1) - 4 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change signs when combining terms
Don't combine x + 8 + 3x - 4 and get 4x + 12 = wrong result! The minus sign affects the 4, making it -4, not +4. Always keep track of positive and negative signs when combining like terms.

Practice Quiz

Test your knowledge with interactive questions

Solve for $$ b $$ :

$$ 8-b=6 $$

FAQ

Everything you need to know about this question

What are 'like terms' exactly?

Like terms have the same variable part. In this equation, $x$ and $3x$ are like terms because they both have x. The constants 8 and -4 are also like terms because they have no variables.

Why do I combine like terms first?

Combining like terms simplifies the equation and makes it easier to solve. Instead of working with 4 separate terms, you get just 2 terms: $4x + 4 = 0$ .

How do I handle the negative sign in front of 4?

The equation is $x + 8 + 3x - 4$ , so you're adding 8 and subtracting 4. Think of it as $8 + (-4) = 4$ .

What if I get a different answer?

Double-check your sign tracking and combining steps! The most common errors happen when combining constants or coefficients. Remember: $x + 3x = 4x$ (not 3x) and $8 - 4 = 4$ (not 12).

Can I solve this equation in a different order?

Yes! You could move terms to different sides first, but combining like terms first is usually easier and less error-prone. It keeps your work organized and clear.

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