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

Q: Why is the answer negative when both numbers in the equation are positive?

Great observation! Even though 9 and 3 are positive, we're subtracting 9 from 3, which gives us a negative result. Remember: $ 3 - 9 = -6 $

Q: How do I know whether to add or subtract 9?

Look at what's happening to x! Since x is being added to 9 (x + 9), you need to do the opposite operation - subtract 9 from both sides to cancel it out.

Q: How can I check my answer?

Substitute your answer back into the original equation: $ (-6) + 9 = 3 $. Since this equals 3, your answer is correct!

Linear Equations with Negative Solutions

Solve for X:

$x + 9 = 3$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$x + 9 = 3$

Step-by-step solution

To solve the equation $x + 9 = 3$ , we need to isolate $x$ .

Step 1: Subtract 9 from both sides of the equation to cancel out the +9 on the left side.
$x + 9 - 9 = 3 - 9$
Step 2: Simplify both sides.
$x = -6$
Thus, the solution is $x = -6$ .

Final Answer

$-6$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Use inverse operations to isolate the variable
Technique: Subtract 9 from both sides: 3 - 9 = -6
Check: Substitute back: (-6) + 9 = 3 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting to isolate x
Don't add 9 to both sides when you see x + 9 = 3! This gives x = 12, which is completely wrong. The +9 is already with x, so you need to subtract 9 from both sides to cancel it out and isolate x.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why is the answer negative when both numbers in the equation are positive?

Great observation! Even though 9 and 3 are positive, we're subtracting 9 from 3, which gives us a negative result. Remember: $3 - 9 = -6$

How do I know whether to add or subtract 9?

Look at what's happening to x! Since x is being added to 9 (x + 9), you need to do the opposite operation - subtract 9 from both sides to cancel it out.

Can I move the 9 to the other side instead?

Yes! When you "move" a term across the equals sign, it changes sign. So x + 9 = 3 becomes $x = 3 - 9$ , giving the same answer: x = -6.

What if I got x = 6 instead of x = -6?

You likely added 9 to both sides instead of subtracting. Remember: to undo addition, you must subtract. Always do the opposite operation!

How can I check my answer?

Substitute your answer back into the original equation: $(-6) + 9 = 3$ . Since this equals 3, your answer is correct!

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