Solve the Fraction Equation: Finding X in 1/6x - 1/3 = 1/3

Q: Why multiply by 6 instead of a different number?

We use 6 because it's the LCD of denominators 6 and 3. The LCD is the smallest number that all denominators divide into evenly, making all fractions disappear in one step!

Q: What if I forget to multiply a term by 6?

You'll get the wrong answer! For example, if you only multiply $ \frac{1}{6}x $ by 6, you get $ x - \frac{1}{3} = \frac{1}{3} $, leading to $ x = \frac{2}{3} $ instead of the correct answer 4.

Q: Can I add fractions instead of using the LCD method?

Yes, but it's much harder! You'd need to get common denominators for $ \frac{1}{3} + \frac{1}{3} $ first. The LCD method is faster and less error-prone for equations with fractions.

Q: How do I check my answer with fractions?

Substitute your answer back into the original equation. For x = 4: $ \frac{1}{6}(4) - \frac{1}{3} = \frac{4}{6} - \frac{2}{6} = \frac{2}{6} = \frac{1}{3} $ ✓

Linear Equations with Fractional Coefficients

Solve for X:

$\frac{1}{6}x-\frac{1}{3}=\frac{1}{3}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 We'll arrange the equation so that one side has only the unknown X

00:22 We'll reduce what we can

00:33 We'll isolate the unknown X, and calculate

00:53 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$\frac{1}{6}x-\frac{1}{3}=\frac{1}{3}$

Step-by-step solution

To solve the equation $\frac{1}{6}x - \frac{1}{3} = \frac{1}{3}$ , we will take the following steps:

Step 1: Eliminate fractions by multiplying the entire equation by the least common multiple of the denominators $6$ .
Step 2: Simplify the resulting equation.
Step 3: Isolate the variable $x$ .

Let's proceed with the solution:

Step 1: Multiply the entire equation by $6$ to clear fractions:
$6 \left(\frac{1}{6}x - \frac{1}{3}\right) = 6 \times \frac{1}{3}$

Step 2: Simplify:
$x - 2 = 2$

Step 3: Solve for $x$ by adding $2$ to both sides:
$x = 2 + 2$

Therefore, $x = 4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

LCD Method: Multiply entire equation by 6 to clear all fractions
Technique: $6 \times \frac{1}{6}x = x$ and $6 \times \frac{1}{3} = 2$
Check: Substitute x = 4: $\frac{1}{6}(4) - \frac{1}{3} = \frac{2}{3} - \frac{1}{3} = \frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only some terms by the LCD
Don't multiply just $\frac{1}{6}x$ by 6 and leave $\frac{1}{3}$ unchanged = unbalanced equation! This breaks the equality because you're not doing the same operation to both sides. Always multiply every single term on both sides by the LCD.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ x - 3 + 5 = 8 - 2 $$

FAQ

Everything you need to know about this question

Why multiply by 6 instead of a different number?

We use 6 because it's the LCD of denominators 6 and 3. The LCD is the smallest number that all denominators divide into evenly, making all fractions disappear in one step!

What if I forget to multiply a term by 6?

You'll get the wrong answer! For example, if you only multiply $\frac{1}{6}x$ by 6, you get $x - \frac{1}{3} = \frac{1}{3}$ , leading to $x = \frac{2}{3}$ instead of the correct answer 4.

Can I add fractions instead of using the LCD method?

Yes, but it's much harder! You'd need to get common denominators for $\frac{1}{3} + \frac{1}{3}$ first. The LCD method is faster and less error-prone for equations with fractions.

How do I check my answer with fractions?

Substitute your answer back into the original equation. For x = 4: $\frac{1}{6}(4) - \frac{1}{3} = \frac{4}{6} - \frac{2}{6} = \frac{2}{6} = \frac{1}{3}$ ✓

What if my LCD is really big?

That's okay! Even with large LCDs, this method works. Just be extra careful with your arithmetic, and consider simplifying fractions along the way to keep numbers manageable.

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Solve the Fraction Equation: Finding X in 1/6x - 1/3 = 1/3

Linear Equations with Fractional Coefficients

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why multiply by 6 instead of a different number?

What if I forget to multiply a term by 6?

Can I add fractions instead of using the LCD method?

How do I check my answer with fractions?

What if my LCD is really big?

🌟 Unlock Your Math Potential

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