Simple Equation Solving: Calculate X in 5 - X = 4

Linear Equations with Isolation Techniques

Solve for X:

5−x=4 5-x=4

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:10 Isolate the unknown X
00:20 Collect like terms
00:24 Convert from negative to positive
00:40 Negative times negative always equals positive
00:44 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 for X:

5−x=4 5-x=4

2

Step-by-step solution

To solve the equation 5−x=45 - x = 4, we aim to isolate xx on one side of the equation.

We start by considering the equation:
5−x=45 - x = 4

Step 1: Eliminate 5 from the left side to isolate terms involving xx. To do this, subtract 5 from both sides of the equation:

(5−x)−5=4−5(5 - x) - 5 = 4 - 5

Step 2: Simplify both sides:

−x=−1-x = -1

Step 3: To solve for xx, multiply or divide both sides by −1-1 to change the sign of xx:

−1⋅−x=−1⋅−1-1 \cdot -x = -1 \cdot -1

This simplifies to:

x=1x = 1

Therefore, the solution to the equation 5−x=45 - x = 4 is x=1x = 1.

The correct answer is x=1x = 1.

3

Final Answer

1

Key Points to Remember

Essential concepts to master this topic
  • Goal: Isolate x by performing same operation on both sides
  • Technique: Subtract 5 from both sides: 5 - x - 5 = 4 - 5
  • Check: Substitute x = 1 back: 5 - 1 = 4 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting when eliminating constants
    Don't add 5 to both sides to get -x = 9, then x = -9! This moves terms in the wrong direction and creates incorrect solutions. Always subtract the constant term from both sides to properly isolate the variable.

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 subtract 5 from both sides instead of adding?

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We have +5 on the left side, so we need to do the opposite operation (subtract 5) to cancel it out. Think of it as undoing what's already there!

What do I do with the negative x?

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When you get −x=−1 -x = -1 , multiply both sides by -1 to make x positive. Remember: negative times negative equals positive!

Can I move the x to the right side instead?

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Yes! Add x to both sides: 5=4+x 5 = 4 + x , then subtract 4: x=1 x = 1 . Both methods work perfectly fine.

How do I check if x = 1 is correct?

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Substitute back into the original equation: 5−1=4 5 - 1 = 4 . Since 4 = 4 is true, your answer is correct!

What if I get a different answer?

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Double-check each step! Common errors include sign mistakes or forgetting to do the same operation to both sides. Practice makes perfect!

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