Solve for X: Finding the Variable in 72-x=63

Linear Equations with Sign Changes

Solve the following exercise:

72x=63 72-x=63

x=? x=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's isolate the unknown X, and calculate
00:15 Convert from negative to positive
00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

72x=63 72-x=63

x=? x=\text{?}

2

Step-by-step solution

To solve the question, we need to isolate X.

Since in this case X is negative, we will move it to the other side.

(Remember that when moving terms between sides, their signs change - from positive to negative and from negative to positive).

72=63+x 72=63+x

Now, we will also move the 63 to the other side.

(Remember that 63 becomes negative when moving sides).

7263=x 72-63=x

And now let's solve the subtraction exercise:

9=x 9=x

3

Final Answer

9 9

Key Points to Remember

Essential concepts to master this topic
  • Rule: When moving terms across equals sign, flip their signs
  • Technique: Move -x to right: 72 = 63 + x
  • Check: Substitute back: 72 - 9 = 63 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to change signs when moving terms
    Don't move -x to the right side and keep it as -x = wrong equation! This creates 72 = 63 - x instead of 72 = 63 + x, giving you x = -9. Always flip the sign when crossing the equals sign.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why does the sign change when I move a term?

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Think of it as adding the opposite to both sides! When you have 72x=63 72 - x = 63 , adding +x to both sides gives 72=63+x 72 = 63 + x .

Can I solve this by moving 63 first instead?

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Absolutely! You could subtract 63 from both sides first: 9x=0 9 - x = 0 , then add x to both sides: 9=x 9 = x . Same answer!

How do I remember which sign to use?

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Use the "opposite rule": if a term is positive on one side, it becomes negative on the other side. If it's negative (like -x), it becomes positive (+x).

What if I get a negative answer?

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Negative answers are completely normal! Always check your work by substituting back. If x=5 x = -5 , then 72(5)=72+5=77 72 - (-5) = 72 + 5 = 77 .

Is there a faster way to solve this?

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Once you understand sign changes, you can think: "What number minus from 72 gives 63?" That's 729=63 72 - 9 = 63 , so x=9 x = 9 !

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