Solve the Linear Equation: 5b + 300b = 0 Step-by-Step

Q: Why can't I just divide 5b by 5 and 300b by 300?

Because 5b and 300b are like terms that must be combined first! You can't split them apart when they're being added together. Think of it like 5 apples + 300 apples = 305 apples.

Q: How do I know when terms are 'like terms'?

Like terms have the same variable with the same exponent. Both 5b and 300b have the variable 'b' to the first power, so they're like terms that can be combined.

Q: Why is the answer 0 and not some fraction?

When you have $ 305b = 0 $, the only way this equation is true is if b = 0. Any non-zero number times 305 would give a non-zero result!

Q: What if the coefficients were different, like 2b + 3b?

Same process! Add the coefficients: 2b + 3b = (2 + 3)b = 5b. The key is always combining coefficients of like terms first.

Q: Can I check my answer a different way?

Yes! Besides substitution, you can think logically: any number times zero equals zero. Since 305 ≠ 0, the variable b must equal 0 for the equation to be satisfied.

Combining Like Terms with Variable Coefficients

$5b+300b=0$

$b=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Factoring

00:07 We want to isolate the unknown B

00:10 Let's isolate the unknown B

00:13 0 divided by any number is always equal to 0

00:17 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

$5b+300b=0$

$b=\text{?}$

Step-by-step solution

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

Step 1: Identify the like terms on the left-hand side of the equation.
Step 2: Combine like terms.
Step 3: Simplify the equation.
Step 4: Solve the equation for $b$ .

Now, let's work through each step:

Step 1: The given equation is $5b + 300b = 0$ .

Step 2: Combine like terms:

$5b + 300b = (5 + 300)b = 305b$

So, the equation becomes $305b = 0$ .

Step 3: Since $305b = 0$ , we can solve for $b$ using the property of zero product:

If $305 \times b = 0$ , then $b$ must be $0$ because $305 \neq 0$ .

Therefore, the solution to the problem is $b = 0$ .

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Rule: Add coefficients of like terms: 5b + 300b = 305b
Technique: Combine coefficients first: (5 + 300)b = 305b
Check: Substitute b = 0: 5(0) + 300(0) = 0 + 0 = 0 ✓

Common Mistakes

Avoid these frequent errors

Solving without combining like terms first
Don't try to solve 5b + 300b = 0 by dividing each term separately = wrong setup! This creates confusion and incorrect steps. Always combine like terms first to get 305b = 0, then solve for b.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why can't I just divide 5b by 5 and 300b by 300?

Because 5b and 300b are like terms that must be combined first! You can't split them apart when they're being added together. Think of it like 5 apples + 300 apples = 305 apples.

How do I know when terms are 'like terms'?

Like terms have the same variable with the same exponent. Both 5b and 300b have the variable 'b' to the first power, so they're like terms that can be combined.

Why is the answer 0 and not some fraction?

When you have $305b = 0$ , the only way this equation is true is if b = 0. Any non-zero number times 305 would give a non-zero result!

What if the coefficients were different, like 2b + 3b?

Same process! Add the coefficients: 2b + 3b = (2 + 3)b = 5b. The key is always combining coefficients of like terms first.

Can I check my answer a different way?

Yes! Besides substitution, you can think logically: any number times zero equals zero. Since 305 ≠ 0, the variable b must equal 0 for the equation to be satisfied.

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