Solve the Equation: 10x = 6/11 and Find X

Q: Why do I divide both sides by 10?

Because we need to isolate x by itself! Since we have $ 10x $, we divide by 10 to get just $ x $. Whatever we do to one side, we must do to the other side too.

Q: How do I divide a fraction by a whole number?

When dividing $ \frac{6}{11} \div 10 $, multiply the denominator by 10: $ \frac{6}{11 \times 10} = \frac{6}{110} $. Never multiply the numerator!

Q: Do I always need to simplify fractions?

Yes! Always reduce fractions to lowest terms. Find the GCD of numerator and denominator. Here, GCD(6,110) = 2, so $ \frac{6}{110} = \frac{3}{55} $.

Q: Can I convert the fraction to a decimal instead?

You could, but exact fractional answers are usually preferred in math class. Decimals might be rounded and less precise than the exact fraction $ \frac{3}{55} $.

Linear Equations with Fractional Solutions

Solve for X:

$10x=\frac{6}{11}$

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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

00:08 If we have an unknown with coefficient A equal to fraction (C divided by B)

00:12 To isolate the unknown X, divide by coefficient A

00:16 We will use this formula in our exercise

00:24 Let's arrange the equation so that one side has only the unknown X

00:32 Let's factor 6 into 2 and 3

00:38 Let's factor 10 into 2 and 5

00:45 Let's reduce what we can

00:48 Let's calculate the denominator

00:52 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:

$10x=\frac{6}{11}$

Step-by-step solution

To solve this problem, we need to isolate $x$ by performing the following steps:

Step 1: Start with the given equation $10x = \frac{6}{11}$ .
Step 2: Divide both sides of the equation by 10 to solve for $x$ . $x = \frac{\frac{6}{11}}{10}$
Step 3: Simplify the fraction on the right. Dividing a fraction by a whole number involves multiplying the denominator by that number: $x = \frac{6}{11 \times 10} = \frac{6}{110}$
Step 4: Reduce the fraction $\frac{6}{110}$ . The greatest common divisor of 6 and 110 is 2: $x = \frac{6 \div 2}{110 \div 2} = \frac{3}{55}$

Thus, the solution to the problem is $x = \frac{3}{55}$ .

Final Answer

$\frac{3}{55}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both sides by the coefficient to isolate x
Technique: Divide fraction by whole number: $\frac{6}{11} \div 10 = \frac{6}{110}$
Check: Substitute back: $10 \times \frac{3}{55} = \frac{30}{55} = \frac{6}{11}$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting 10 instead of dividing
Don't try to move 10 to the other side by adding or subtracting = wrong operation! This gives answers like $\frac{6}{11} - 10$ which doesn't solve for x. Always divide both sides by the coefficient of x.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I divide both sides by 10?

Because we need to isolate x by itself! Since we have $10x$ , we divide by 10 to get just $x$ . Whatever we do to one side, we must do to the other side too.

How do I divide a fraction by a whole number?

When dividing $\frac{6}{11} \div 10$ , multiply the denominator by 10: $\frac{6}{11 \times 10} = \frac{6}{110}$ . Never multiply the numerator!

Do I always need to simplify fractions?

Yes! Always reduce fractions to lowest terms. Find the GCD of numerator and denominator. Here, GCD(6,110) = 2, so $\frac{6}{110} = \frac{3}{55}$ .

What if I get a really small fraction as my answer?

That's completely normal! Some equations naturally have very small fractional solutions. Just make sure you've simplified correctly and double-check by substituting back into the original equation.

Can I convert the fraction to a decimal instead?

You could, but exact fractional answers are usually preferred in math class. Decimals might be rounded and less precise than the exact fraction $\frac{3}{55}$ .

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