Solve for Y: Finding the Value in y-4=9

Q: Why do I need to add 4 to both sides?

An equation is like a balanced scale. Whatever you do to one side, you must do to the other to keep it balanced. Adding 4 to only one side would tip the scale!

Q: What if I subtract 9 from both sides instead?

You'd get $ y - 4 - 9 = 0 $, which gives $ y - 13 = 0 $, so $ y = 13 $. Same answer, but adding 4 is more direct!

Q: How do I know which operation to use?

Look at what's happening to your variable. Since 4 is being subtracted from y, do the opposite operation (add 4) to cancel it out.

Q: Can I check my answer a different way?

Yes! You can also think: "What number minus 4 equals 9?" Count up from 9: 9 + 4 = 13. So y = 13 makes sense!

Linear Equations with Addition Property

Solve for Y:

$y-4=9$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for Y:

$y-4=9$

Step-by-step solution

To solve for $y$ , we need to isolate it on one side of the equation. Starting with:

$y-4=9$

Add $4$ to both sides to get:

$y-4+4=9+4$

This simplifies to:

$y=13$

Therefore, the solution is $y = 13$ .

Final Answer

$13$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Add the opposite to eliminate terms from one side
Technique: Add 4 to both sides: y - 4 + 4 = 9 + 4
Check: Substitute back: 13 - 4 = 9, which equals 9 ✓

Common Mistakes

Avoid these frequent errors

Adding 4 to only one side of the equation
Don't add 4 just to the left side = y = 9 + 4 = 13, but the original equation becomes unbalanced! This breaks the equality principle. Always perform the same operation on both sides of the equation.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to add 4 to both sides?

An equation is like a balanced scale. Whatever you do to one side, you must do to the other to keep it balanced. Adding 4 to only one side would tip the scale!

What if I subtract 9 from both sides instead?

You'd get $y - 4 - 9 = 0$ , which gives $y - 13 = 0$ , so $y = 13$ . Same answer, but adding 4 is more direct!

How do I know which operation to use?

Look at what's happening to your variable. Since 4 is being subtracted from y, do the opposite operation (add 4) to cancel it out.

Can I check my answer a different way?

Yes! You can also think: "What number minus 4 equals 9?" Count up from 9: 9 + 4 = 13. So y = 13 makes sense!

What if my answer doesn't check out?

Go back and check your arithmetic! Make sure you added the same number to both sides and calculated correctly. Don't panic - just retrace your steps.

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