Solve the Linear Equation: b + 2b + 4 = 0

Q: How do I combine b and 2b together?

Think of b as 1b, so you have $ 1b + 2b = 3b $. It's like saying 1 apple + 2 apples = 3 apples!

Q: Why is my answer a mixed number?

When you get $ b = -\frac{4}{3} $, you can convert it to the mixed number $ -1\frac{1}{3} $. Both forms are correct, but mixed numbers are often easier to understand!

Q: Can I leave my answer as an improper fraction?

Yes! $ -\frac{4}{3} $ and $ -1\frac{1}{3} $ are the same value. However, check what form your teacher or textbook prefers for the final answer.

Q: What does it mean when the answer is negative?

A negative solution just means the variable has a negative value. This is completely normal! Always include the negative sign in your final answer.

Q: How do I check if -1⅓ is really correct?

Substitute back: $ (-1\frac{1}{3}) + 2(-1\frac{1}{3}) + 4 = -1\frac{1}{3} - 2\frac{2}{3} + 4 = -4 + 4 = 0 $ ✓

Linear Equations with Mixed Number Solutions

$b+2b+4=0$

$b=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find B

00:03 Collect terms

00:08 Arrange the equation so that one side has only the unknown B

00:17 Isolate B

00:26 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

$b+2b+4=0$

$b=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Simplify the equation by combining like terms.
Step 2: Isolate the variable $b$ on one side of the equation.
Step 3: Solve for the value of $b$ .

Now, let's work through these steps:
Step 1: Combine the terms $b$ and $2b$ to simplify the equation:
$b + 2b + 4 = 0$ becomes $3b + 4 = 0$ .

Step 2: Isolate the variable $b$ by subtracting 4 from both sides:
$3b + 4 - 4 = 0 - 4$ simplifies to $3b = -4$ .

Step 3: Solve for $b$ by dividing both sides by 3:
$b = \frac{-4}{3}$ .

The solution to the problem is $b = -1\frac{1}{3}$ .

Therefore, choice 4 is the correct option: $-1\frac{1}{3}$ .

Final Answer

$-1\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Add coefficients of same variables before solving
Technique: $b + 2b = 3b$ then isolate variable
Check: Substitute $b = -1\frac{1}{3}$ : $3(-\frac{4}{3}) + 4 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Not combining like terms first
Don't try to solve $b + 2b + 4 = 0$ without combining $b$ and $2b$ first = confusing multiple steps! This makes the problem unnecessarily complicated and leads to errors. Always combine like terms first to get $3b + 4 = 0$ .

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

How do I combine b and 2b together?

Think of b as 1b, so you have $1b + 2b = 3b$ . It's like saying 1 apple + 2 apples = 3 apples!

Why is my answer a mixed number?

When you get $b = -\frac{4}{3}$ , you can convert it to the mixed number $-1\frac{1}{3}$ . Both forms are correct, but mixed numbers are often easier to understand!

Can I leave my answer as an improper fraction?

Yes! $-\frac{4}{3}$ and $-1\frac{1}{3}$ are the same value. However, check what form your teacher or textbook prefers for the final answer.

What does it mean when the answer is negative?

A negative solution just means the variable has a negative value. This is completely normal! Always include the negative sign in your final answer.

How do I check if -1⅓ is really correct?

Substitute back: $(-1\frac{1}{3}) + 2(-1\frac{1}{3}) + 4 = -1\frac{1}{3} - 2\frac{2}{3} + 4 = -4 + 4 = 0$ ✓

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