Solve Linear Equation: Finding 'a' in 2+3a+4=0

Q: Why do I need to combine the constants first?

Combining constants simplifies your equation! Instead of juggling three separate terms (2, 3a, and 4), you work with just two terms (3a and 6). This makes the next steps much clearer.

Q: What if I solve without combining constants first?

You'll still get the right answer, but it's much harder! You'd need to subtract both 2 and 4 from each side separately. Always combine first to make your work easier.

Q: How do I know which terms to combine?

Combine terms that are alike! Constants (plain numbers) combine with constants, and terms with the same variable combine with each other. Here, 2 and 4 are both constants.

Linear Equations with Constant Terms

$2+3a+4=0$

$a=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown A

00:07 We'll arrange the equation so that one side will have only the unknown A

00:19 Let's isolate the unknown A

00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2+3a+4=0$

$a=\text{?}$

Step-by-step solution

To solve the equation $2 + 3a + 4 = 0$ , follow these steps:

Step 1: Combine the constant terms on the left side.
The terms $2$ and $4$ can be combined to get $6$ .
Hence, the equation becomes $3a + 6 = 0$ .
Step 2: Isolate the term with the variable $a$ .
Subtract $6$ from both sides to get $3a = -6$ .
Step 3: Solve for $a$ by dividing both sides by the coefficient of $a$ , which is $3$ .
Thus, $a = \frac{-6}{3} = -2$ .

Therefore, the solution to the problem is $a = -2$ .

Final Answer

$-2$

Key Points to Remember

Essential concepts to master this topic

Combining: Add constant terms first before isolating the variable
Technique: Combine 2 + 4 = 6, then solve 3a + 6 = 0
Check: Substitute back: 2 + 3(-2) + 4 = 2 - 6 + 4 = 0 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms first
Don't work with 2 + 3a + 4 = 0 as separate terms = harder calculations and confusion! This makes the problem unnecessarily complex. Always combine constants first: 2 + 4 = 6, giving you 3a + 6 = 0.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I need to combine the constants first?

Combining constants simplifies your equation! Instead of juggling three separate terms (2, 3a, and 4), you work with just two terms (3a and 6). This makes the next steps much clearer.

What if I solve without combining constants first?

You'll still get the right answer, but it's much harder! You'd need to subtract both 2 and 4 from each side separately. Always combine first to make your work easier.

How do I know which terms to combine?

Combine terms that are alike! Constants (plain numbers) combine with constants, and terms with the same variable combine with each other. Here, 2 and 4 are both constants.

What if my final answer is negative?

Negative answers are completely normal! Many linear equations have negative solutions. Just make sure to double-check by substituting back into the original equation.

Can I move terms around differently?

Yes! You could subtract 2 and 4 separately from both sides. However, combining first reduces your steps and minimizes calculation errors.

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