Solve for X in the Linear Equation: -9-x = 3+2x

Q: Why do I need to move all the x terms to one side?

Moving all variable terms to one side lets you combine them into a single term like 3x. This makes it much easier to solve for x by dividing both sides by the coefficient.

Q: What happens if I forget to change the sign when moving a term?

You'll get the wrong answer! When you move a term across the equals sign, it's like adding the opposite to both sides. So -x becomes +x, and +3 becomes -3.

Q: Can I check my answer a different way?

Yes! You can also work backwards. Start with your answer x = -4, then substitute it into each side separately: Left side = -9-(-4) = -5, Right side = 3+2(-4) = -5. Both equal -5! ✓

Q: What if I get a fraction when dividing?

That's normal! Many linear equations have fractional solutions. Just make sure to simplify the fraction to lowest terms and always verify your answer.

Linear Equations with Variable Collection

Solve for x:

$-9-x=3+2x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Let's arrange the equation so that one side has only the unknown X

00:16 Group like terms

00:21 Isolate X

00:27 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$-9-x=3+2x$

Step-by-step solution

To solve the equation, we will move similar elements to one side.

On the right side, we place the elements with X, while in the left side we place the elements without X.

Remember that when we move sides, the plus and minus signs change accordingly, so we get:

$-9-3=2x+x$

We calculate both sides: $-12=3x$

Finally, divide both sides by 3:

$-\frac{12}{3}=\frac{3x}{3}$

$-4=x$

Final Answer

-4

Key Points to Remember

Essential concepts to master this topic

Rule: Move all variable terms to one side, constants to the other
Technique: Change signs when moving: -x becomes +x across the equals
Check: Substitute x = -4: -9-(-4) = 3+2(-4) gives -5 = -5 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change signs when moving terms
Don't move -x to the right side as -x = wrong equation! This keeps the negative sign and gives x = 4 instead of x = -4. Always change the sign when moving any term across the equals sign.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I need to move all the x terms to one side?

Moving all variable terms to one side lets you combine them into a single term like 3x. This makes it much easier to solve for x by dividing both sides by the coefficient.

What happens if I forget to change the sign when moving a term?

You'll get the wrong answer! When you move a term across the equals sign, it's like adding the opposite to both sides. So -x becomes +x, and +3 becomes -3.

How do I know which side to put the x terms on?

It doesn't matter! You can put x terms on either side. Choose whichever side makes the coefficient of x positive - it's usually easier to work with.

Can I check my answer a different way?

Yes! You can also work backwards. Start with your answer x = -4, then substitute it into each side separately: Left side = -9-(-4) = -5, Right side = 3+2(-4) = -5. Both equal -5! ✓

What if I get a fraction when dividing?

That's normal! Many linear equations have fractional solutions. Just make sure to simplify the fraction to lowest terms and always verify your answer.

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