Solve for b in 2b-3b+4=5: Linear Equation Solution

Q: Why does 2b - 3b equal -1b and not 1b?

Think of it like money: if you have 2 dollars but owe 3 dollars, you're 1 dollar in debt (negative). Similarly, $ 2b - 3b = -1b $.

Q: Do I have to write -1b or can I write -b?

Both are correct! $ -1b $ and $ -b $ mean exactly the same thing. Most students find it clearer to write -1b when learning.

Q: How do I know which terms to move first?

It doesn't matter! You can move the variable terms to one side and number terms to the other, or do it the opposite way. Both methods work perfectly.

Q: What if I get confused about the signs when moving terms?

Use this trick: instead of moving terms, add or subtract the same thing from both sides. For example, subtract 4 from both sides rather than "moving" the 4.

Q: Why do we divide by -1 at the end?

Because we want $ b $ by itself, not $ -1b $. Dividing both sides by -1 gives us $ b = -1 $, which is our final answer.

Linear Equations with Like Term Combining

$2b-3b+4=5$

$b=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown B

00:08 Let's collect terms

00:16 Convert from negative to positive

00:24 Negative divided by negative always equals positive

00:28 Positive divided by negative always equals negative

00:31 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

$2b-3b+4=5$

$b=\text{?}$

Step-by-step solution

Let's first arrange the equation so that on the left-hand side we have the terms with the coefficient $b$ and on the right-hand side the numbers without the coefficient $b$ .

Remember that when we move terms across the equals sign, the plus and minus signs will change accordingly:

$2b-3b=5-4$

Let's now solve the subtraction exercise on both sides:

$-1b=1$

Finally, we can divide both sides by -1 to find our answer:

$b=-1$

Final Answer

-1

Key Points to Remember

Essential concepts to master this topic

Combining: Add or subtract coefficients of like terms first
Technique: $2b-3b$ becomes $-1b$ or $-b$
Check: Substitute $b=-1$ : $2(-1)-3(-1)+4=5$ ✓

Common Mistakes

Avoid these frequent errors

Moving terms incorrectly across the equals sign
Don't move 4 to the right side as +4 = wrong answer! When moving terms across the equals sign, you must change their signs. Always remember: +4 becomes -4 when moved across.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why does 2b - 3b equal -1b and not 1b?

Think of it like money: if you have 2 dollars but owe 3 dollars, you're 1 dollar in debt (negative). Similarly, $2b - 3b = -1b$ .

Do I have to write -1b or can I write -b?

Both are correct! $-1b$ and $-b$ mean exactly the same thing. Most students find it clearer to write -1b when learning.

How do I know which terms to move first?

It doesn't matter! You can move the variable terms to one side and number terms to the other, or do it the opposite way. Both methods work perfectly.

What if I get confused about the signs when moving terms?

Use this trick: instead of moving terms, add or subtract the same thing from both sides. For example, subtract 4 from both sides rather than "moving" the 4.

Why do we divide by -1 at the end?

Because we want $b$ by itself, not $-1b$ . Dividing both sides by -1 gives us $b = -1$ , which is our final answer.

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