Solve for X in the Equation: x + 5 = 11x - Step by Step

Linear Equations with Variable Isolation

Solve for X:

x+5=11x x+5=11x

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve the problem together!
00:09 First, we need to isolate the unknown variable, X.
00:26 Next, let's simplify or reduce as much as we can for clarity.
00:41 We can write any division as a fraction.
00:49 Factorize ten into two times five.
00:56 Again, reduce where possible.
01:02 And there you have it, the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

x+5=11x x+5=11x

2

Step-by-step solution

Let's solve the equation x+5=11x x + 5 = 11x step-by-step.

  • Step 1: Isolate the variable x x
    Start by getting all terms involving x x on one side of the equation. We can do this by subtracting x x from both sides:
    x+5x=11xx x + 5 - x = 11x - x
  • This simplifies to:
    5=10x 5 = 10x
  • Step 2: Solve for x x
    Now, divide both sides of the equation by 10 to solve for x x :
    510=10x10 \frac{5}{10} = \frac{10x}{10}
  • This further simplifies to:
    x=12 x = \frac{1}{2}

Therefore, the solution to the equation x+5=11x x + 5 = 11x is x=12 x = \frac{1}{2} .

3

Final Answer

12 \frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Move all terms with variables to one side first
  • Technique: Subtract x from both sides: x + 5 - x = 11x - x becomes 5 = 10x
  • Check: Substitute 12 \frac{1}{2} back: 12+5=1112 \frac{1}{2} + 5 = 11 \cdot \frac{1}{2} gives 5.5=5.5 5.5 = 5.5

Common Mistakes

Avoid these frequent errors
  • Adding x to both sides instead of subtracting
    Don't add x to both sides to get 2x + 5 = 12x = wrong setup! This makes more variable terms instead of fewer. Always subtract the smaller variable term from both sides to collect variables on one side.

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 x from both sides instead of adding?

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You want to eliminate the variable from one side, not create more variable terms! Since we have x on the left and 11x on the right, subtracting x removes it from the left side completely.

Can I move the 5 first instead of the x?

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Yes, but it's usually easier to move variables first! If you subtract 5 from both sides first, you get x=11x5 x = 11x - 5 , which still requires moving variables anyway.

How do I know which variable term to subtract?

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Always subtract the smaller coefficient from both sides. Here, subtract x (coefficient 1) rather than 11x (coefficient 11) to keep positive numbers.

What if I get a fraction as my answer?

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Fractional answers are completely normal! Many linear equations have fractional solutions. Just make sure to simplify the fraction and always verify by substituting back.

Why does x + 5 - x equal just 5?

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Because xx=0 x - x = 0 ! When you have the same term with opposite signs, they cancel out completely, leaving you with just the constant term 5.

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