Solve the Algebraic Equation: 5 + 3 + x + 2x + 1 = 0

Q: What are like terms exactly?

Like terms have the same variable with the same exponent. In this problem, 5, 3, and 1 are like terms (all constants), and x and 2x are like terms (both have x to the first power).

Q: Why do I combine like terms before solving?

Combining like terms simplifies the equation and reduces errors. Instead of working with 5 separate terms, you get a cleaner equation like $ 9 + 3x = 0 $ that's easier to solve!

Q: How do I know which terms to combine?

Look for terms that are exactly the same type: all plain numbers go together, all x-terms go together, all $ x^2 $ terms go together, etc. Different variable powers cannot be combined.

Linear Equations with Multiple Like Terms

$5+3+x+2x+1=0$

$x=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 First, we need to find X.

00:11 Let's collect all the terms together.

00:20 Next, arrange the equation so X stands alone on one side.

00:32 Now, let's isolate X.

00:40 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5+3+x+2x+1=0$

$x=\text{?}$

Step-by-step solution

Let's solve the equation step by step:

First, we identify the terms in the equation: $5$ , $3$ , $x$ , $2x$ , and $1$ .
Combine like terms on the left side of the equation:

The constant terms: $5 + 3 + 1 = 9$ .
The terms with $x$ : $x + 2x = 3x$ .

Substitute back into the equation to get $9 + 3x = 0$ .
Isolate the term containing $x$ by subtracting 9 from both sides: $3x = -9$ .
Solve for $x$ by dividing both sides by 3: $x = \frac{-9}{3}$ .
Simplify the fraction: $x = -3$ .

Therefore, the solution to the equation is $x = -3$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Group constants and variables separately before solving
Technique: 5 + 3 + 1 = 9 and x + 2x = 3x
Check: Substitute x = -3: 9 + 3(-3) = 0 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms first
Don't try to isolate x without combining like terms = messy calculations and errors! This makes the problem unnecessarily complicated and leads to mistakes. Always combine all constants together and all x-terms together first.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

What are like terms exactly?

Like terms have the same variable with the same exponent. In this problem, 5, 3, and 1 are like terms (all constants), and x and 2x are like terms (both have x to the first power).

Why do I combine like terms before solving?

Combining like terms simplifies the equation and reduces errors. Instead of working with 5 separate terms, you get a cleaner equation like $9 + 3x = 0$ that's easier to solve!

How do I know which terms to combine?

Look for terms that are exactly the same type: all plain numbers go together, all x-terms go together, all $x^2$ terms go together, etc. Different variable powers cannot be combined.

What if I get a negative answer?

Negative solutions are completely normal in algebra! Just double-check your work by substituting back into the original equation. If it makes the equation true, your negative answer is correct.

Can I solve this without combining like terms first?

Technically yes, but it's much harder and more error-prone. You'd need to move terms one by one, which creates more steps and opportunities for mistakes. Always combine first!

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