Solve for X in 3x - 1/9 = 8/9: Fraction Equation Solution

Q: Why do I add 1/9 to both sides instead of subtracting it?

Because we have negative 1/9 on the left side! To eliminate it, we need to do the opposite operation. Adding $ \frac{1}{9} $ cancels out the $ -\frac{1}{9} $.

Q: How do I add fractions with the same denominator?

When denominators are the same, just add the numerators and keep the denominator: $ \frac{8}{9} + \frac{1}{9} = \frac{8+1}{9} = \frac{9}{9} = 1 $

Q: Why does 9/9 equal 1?

Any fraction where the numerator equals the denominator equals 1! Think of it as 9 pieces out of 9 total pieces = the whole thing = 1.

Q: What if I get a different denominator when dividing by 3?

When dividing 1 by 3, you get $ \frac{1}{3} $. This fraction is already in simplest form since 1 and 3 share no common factors other than 1.

Q: Can I solve this by multiplying everything by 9 first?

Yes! Multiplying by 9 clears the fractions: $ 27x - 1 = 8 $, then $ 27x = 9 $, so $ x = \frac{9}{27} = \frac{1}{3} $. Both methods work!

Linear Equations with Fractional Constants

Find the value of the parameter X

$3x-\frac{1}{9}=\frac{8}{9}$

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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

00:09 Let's arrange the equation so that one side has only the unknown X

00:21 Let's simplify what we can

00:34 Let's isolate the unknown X and calculate

00:48 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

Find the value of the parameter X

$3x-\frac{1}{9}=\frac{8}{9}$

Step-by-step solution

To find the value of $x$ in the given equation, we will perform the following steps:

Step 1: Start with the equation given: $3x - \frac{1}{9} = \frac{8}{9}$ .
Step 2: To eliminate the constant $-\frac{1}{9}$ on the left, add $\frac{1}{9}$ to both sides:

$3x - \frac{1}{9} + \frac{1}{9} = \frac{8}{9} + \frac{1}{9}$

This simplifies to:

$3x = \frac{8}{9} + \frac{1}{9}$

Combine the fractions on the right side:

$\frac{8}{9} + \frac{1}{9} = \frac{9}{9} = 1$

So, now we have:

$3x = 1$

Step 3: Divide both sides by 3 to solve for $x$ :

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

Thus, the solution to the equation is:

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

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Addition Property: Add the same value to both sides to isolate variable terms
Technique: Combine fractions with same denominator: $\frac{8}{9} + \frac{1}{9} = \frac{9}{9} = 1$
Check: Substitute back: $3(\frac{1}{3}) - \frac{1}{9} = 1 - \frac{1}{9} = \frac{8}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting fractions incorrectly when combining terms
Don't add $\frac{8}{9} + \frac{1}{9} = \frac{8+1}{9+9} = \frac{9}{18}$ ! This gives wrong denominators and incorrect results. Always keep the same denominator when adding fractions: $\frac{8}{9} + \frac{1}{9} = \frac{8+1}{9} = \frac{9}{9} = 1$ .

Practice Quiz

Test your knowledge with interactive questions

$\frac{-y}{5}=-25$

FAQ

Everything you need to know about this question

Why do I add 1/9 to both sides instead of subtracting it?

Because we have negative 1/9 on the left side! To eliminate it, we need to do the opposite operation. Adding $\frac{1}{9}$ cancels out the $-\frac{1}{9}$ .

How do I add fractions with the same denominator?

When denominators are the same, just add the numerators and keep the denominator: $\frac{8}{9} + \frac{1}{9} = \frac{8+1}{9} = \frac{9}{9} = 1$

Why does 9/9 equal 1?

Any fraction where the numerator equals the denominator equals 1! Think of it as 9 pieces out of 9 total pieces = the whole thing = 1.

What if I get a different denominator when dividing by 3?

When dividing 1 by 3, you get $\frac{1}{3}$ . This fraction is already in simplest form since 1 and 3 share no common factors other than 1.

Can I solve this by multiplying everything by 9 first?

Yes! Multiplying by 9 clears the fractions: $27x - 1 = 8$ , then $27x = 9$ , so $x = \frac{9}{27} = \frac{1}{3}$ . Both methods work!

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Solve for X in 3x - 1/9 = 8/9: Fraction Equation Solution

Linear Equations with Fractional Constants

❤️ 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 do I add 1/9 to both sides instead of subtracting it?

How do I add fractions with the same denominator?

Why does 9/9 equal 1?

What if I get a different denominator when dividing by 3?

Can I solve this by multiplying everything by 9 first?

🌟 Unlock Your Math Potential

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