Solve Linear Equation: Finding X in x - 5 = -10

Q: Why do I add 5 when the equation shows minus 5?

Great question! To isolate x, you need to 'undo' what's being done to it. Since 5 is being subtracted from x, you add 5 to both sides to cancel it out.

Q: What if I accidentally subtract 5 from both sides?

You'd get $ x - 10 = -15 $, then $ x = -5 $. Interestingly, you might get the right answer, but your steps would be wrong! Always add the opposite of what you see.

Q: Do I always add to both sides?

Not always! You do the opposite operation. If you see $ x + 3 = 7 $, you'd subtract 3 from both sides. If you see $ x - 3 = 7 $, you'd add 3 to both sides.

Q: How do I check my answer quickly?

Substitute your answer back into the original equation. Replace x with -5: (-5) - 5 = -10. Since -10 = -10, your answer is correct!

Linear Equations with Negative Solutions

Solve for X:

$x - 5 = -10$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$x - 5 = -10$

Step-by-step solution

To solve the equation $x - 5 = -10$ , we need to isolate $x$ .

Step 1: Add 5 to both sides of the equation to cancel out the -5 on the left side.
$x - 5 + 5 = -10 + 5$
Step 2: Simplify both sides.
$x = -5$
Thus, the solution is $x = -5$ .

Final Answer

$-5$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Add or subtract to move numbers away from variable
Technique: Add 5 to both sides: x - 5 + 5 = -10 + 5
Check: Substitute back: (-5) - 5 = -10, which equals -10 ✓

Common Mistakes

Avoid these frequent errors

Subtracting instead of adding to isolate x
Don't subtract 5 from both sides when you see x - 5 = -10! This gives x - 10 = -15, so x = -5, but that's wrong logic. Always do the opposite operation: since we have minus 5, we add 5 to both sides.

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 add 5 when the equation shows minus 5?

Great question! To isolate x, you need to 'undo' what's being done to it. Since 5 is being subtracted from x, you add 5 to both sides to cancel it out.

How can the answer be negative?

Negative answers are completely normal in algebra! Think of it this way: if you start with -5 and subtract 5 more, you get -10. So $x = -5$ makes perfect sense.

What if I accidentally subtract 5 from both sides?

You'd get $x - 10 = -15$ , then $x = -5$ . Interestingly, you might get the right answer, but your steps would be wrong! Always add the opposite of what you see.

Do I always add to both sides?

Not always! You do the opposite operation. If you see $x + 3 = 7$ , you'd subtract 3 from both sides. If you see $x - 3 = 7$ , you'd add 3 to both sides.

How do I check my answer quickly?

Substitute your answer back into the original equation. Replace x with -5: (-5) - 5 = -10. Since -10 = -10, your answer is correct!

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