Solve the Linear Equation: Finding b in 8-b=6

Q: Why can't I just move the negative sign to the other side?

You can't simply "move" a negative sign! The negative is multiplying the variable b, so you need to divide both sides by -1 to isolate b properly.

Q: What's the difference between -b and b with a negative coefficient?

In $ -b $, the coefficient is -1. To solve for b, you must divide both sides by -1, which changes the signs on both sides of the equation.

Q: Can I add b to both sides instead?

Yes! Adding b to both sides gives you $ 8 = 6 + b $, then subtract 6: $ b = 2 $. This is another valid approach!

Q: How do I check if b = 2 is correct?

Substitute back into the original equation: $ 8 - 2 = 6 $. Since 6 = 6 is true, your answer is correct!

Q: What if I get confused about the signs?

Take it step by step! First isolate the variable term (-b), then handle the negative coefficient by dividing both sides by -1. Don't rush the sign changes!

Linear Equations with Negative Variables

Solve for $b$ :

$8-b=6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find B

00:03 Let's arrange the equation so that B is isolated on one side

00:06 Combine like terms

00:09 Convert from negative to positive

00:12 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

Solve for $b$ :

$8-b=6$

Step-by-step solution

First we will move terms so that -b remains remains on the left side of the equation.

We'll move 8 to the right-hand side, making sure to retain the plus and minus signs accordingly:

$-b=6-8$

Then we will subtract as follows:

$-b=-2$

Finally, we will divide both sides by -1 (be careful with the plus and minus signs when dividing by a negative):

$\frac{-b}{-1}=\frac{-2}{-1}$

$b=2$

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Move all terms away from the variable term
Technique: Subtract 8 from both sides: -b = 6 - 8 = -2
Check: Substitute b = 2 back: 8 - 2 = 6 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change signs when dividing by negative one
Don't just remove the negative sign from -b = -2 to get b = -2! This ignores the division step and gives the wrong sign. Always divide both sides by -1: (-b)/(-1) = (-2)/(-1), so b = 2.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why can't I just move the negative sign to the other side?

You can't simply "move" a negative sign! The negative is multiplying the variable b, so you need to divide both sides by -1 to isolate b properly.

What's the difference between -b and b with a negative coefficient?

In $-b$ , the coefficient is -1. To solve for b, you must divide both sides by -1, which changes the signs on both sides of the equation.

Can I add b to both sides instead?

Yes! Adding b to both sides gives you $8 = 6 + b$ , then subtract 6: $b = 2$ . This is another valid approach!

How do I check if b = 2 is correct?

Substitute back into the original equation: $8 - 2 = 6$ . Since 6 = 6 is true, your answer is correct!

What if I get confused about the signs?

Take it step by step! First isolate the variable term (-b), then handle the negative coefficient by dividing both sides by -1. Don't rush the sign changes!

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