Solve the Linear Equation: 2b + 16 + b = -2

Q: What are like terms and why do I combine them first?

Like terms have the same variable with the same exponent. In $ 2b + 16 + b $, the terms $ 2b $ and $ b $ are like terms. Combining them first simplifies the equation and makes it easier to solve!

Q: How do I combine 2b + b? Isn't b just b?

Think of $ b $ as $ 1b $! So $ 2b + b = 2b + 1b = 3b $. It's like saying 2 apples + 1 apple = 3 apples.

Q: Can I move the +16 to the right side instead?

Yes! Moving $ +16 $ to the right changes it to $ -16 $. You'll get $ 3b = -2 - 16 = -18 $, which gives the same answer.

Q: How do I know when to stop solving?

Stop when you have isolated the variable! Your final answer should look like $ b = \text{some number} $, with the variable by itself on one side.

Q: What if I made an error but my check doesn't work?

Go back and carefully redo each step. Check your combining of like terms, your subtraction, and your division. Small arithmetic errors are very common in multi-step problems!

Linear Equations with Like Term Combination

$2b+16+b=-2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find B

00:05 Collect terms

00:10 Arrange the equation so that only the unknown B is on one side

00:14 Collect terms

00:19 Isolate B

00:22 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

$2b+16+b=-2$

Step-by-step solution

To solve the equation $2b + 16 + b = -2$ , we'll follow these steps:

Step 1: Combine like terms on the left side of the equation.
Step 2: Isolate the variable $b$ on one side of the equation.
Step 3: Solve for $b$ .

Now, let's work through each step:

Step 1: Combine the terms with the variable $b$ on the left side. We have $2b + b = 3b$ . Thus, the equation becomes:

$3b + 16 = -2$

Step 2: Subtract 16 from both sides to isolate the term with the variable:

$3b + 16 - 16 = -2 - 16$

Which simplifies to:

$3b = -18$

Step 3: Divide both sides by 3 to solve for $b$ :

$b = \frac{-18}{3}$

The solution is:

$b = -6$

Therefore, the solution to the equation is $b = -6$ , corresponding to choice 1.

Final Answer

$-6$

Key Points to Remember

Essential concepts to master this topic

Rule: Combine like terms first to simplify the equation
Technique: $2b + b = 3b$ before isolating the variable
Check: Substitute $b = -6$ : $2(-6) + 16 + (-6) = -2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms before solving
Don't skip combining $2b + b$ and try to isolate each term separately = complicated, wrong algebra! This makes the equation much harder to solve and often leads to errors. Always combine like terms as your first step to simplify the equation.

Practice Quiz

Test your knowledge with interactive questions

$$ -16+a=-17 $$

FAQ

Everything you need to know about this question

What are like terms and why do I combine them first?

Like terms have the same variable with the same exponent. In $2b + 16 + b$ , the terms $2b$ and $b$ are like terms. Combining them first simplifies the equation and makes it easier to solve!

How do I combine 2b + b? Isn't b just b?

Think of $b$ as $1b$ ! So $2b + b = 2b + 1b = 3b$ . It's like saying 2 apples + 1 apple = 3 apples.

What if I get a positive answer instead of negative?

Double-check your arithmetic! When subtracting 16 from both sides: $-2 - 16 = -18$ (not +18). Negative minus positive equals more negative.

Can I move the +16 to the right side instead?

Yes! Moving $+16$ to the right changes it to $-16$ . You'll get $3b = -2 - 16 = -18$ , which gives the same answer.

How do I know when to stop solving?

Stop when you have isolated the variable! Your final answer should look like $b = \text{some number}$ , with the variable by itself on one side.

What if I made an error but my check doesn't work?

Go back and carefully redo each step. Check your combining of like terms, your subtraction, and your division. Small arithmetic errors are very common in multi-step problems!

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