Solve for X in (3-x)/9 = (4+x)/6: Fraction Equation Practice

Q: Why can I cross-multiply these fractions?

Cross-multiplication works because you have one fraction equals another fraction. When $ \frac{a}{b} = \frac{c}{d} $, multiplying both sides by bd gives you $ ad = bc $!

Q: Should I simplify the fraction -18/15?

Yes! Always simplify fractions to lowest terms. Since $ \gcd(18,15) = 3 $, we get $ -\frac{18}{15} = -\frac{6}{5} $. Both forms are correct, but simplified is preferred.

Q: What if I get confused with the signs when distributing?

Take it step by step! For $ 6(3-x) $: multiply 6×3=18, then 6×(-x)=-6x. Write it as 18-6x, not 18+6x.

Q: How do I check if x = -18/15 is correct?

Substitute back: $ \frac{3-(-\frac{18}{15})}{9} $ should equal $ \frac{4+(-\frac{18}{15})}{6} $. If both sides give the same decimal value, you're right!

Q: Can I solve this by clearing fractions instead?

Absolutely! Multiply everything by the LCD of 18: $ 18 \cdot \frac{3-x}{9} = 18 \cdot \frac{4+x}{6} $ gives $ 2(3-x) = 3(4+x) $. Same answer, different method!

Cross-Multiplication with Algebraic Fractions

Solve for X:

$\frac{3-x}{9}=\frac{4+x}{6}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:05 Multiply by the common denominator to eliminate fractions

00:19 Simplify as much as possible

00:34 Make sure to open parentheses properly, multiply by each factor

00:51 Arrange the equation so that one side only has the unknown X

01:18 Collect like terms

01:27 Isolate X

01:37 Simplify as much as possible

01:41 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$\frac{3-x}{9}=\frac{4+x}{6}$

Step-by-step solution

To solve the equation $\frac{3-x}{9} = \frac{4+x}{6}$ , we will use the method of cross-multiplication to eliminate the fractions.

Step 1: Cross-multiply to get rid of the fractions. This involves multiplying the numerator of each fraction by the denominator of the other:

$(3-x) \times 6 = (4+x) \times 9$

Step 2: Distribute the multiplication over the terms inside the parentheses:

$6(3-x) = 9(4+x)$

$18 - 6x = 36 + 9x$

Step 3: Combine like terms to simplify the equation. Start by getting all the $x$ -terms on one side and the constant terms on the other:

Add $6x$ to both sides: $18 = 36 + 9x + 6x$
Rearrange: $18 = 36 + 15x$
Subtract 36 from both sides: $18 - 36 = 15x$
Result: $-18 = 15x$

Step 4: Solve for $x$ by dividing both sides by 15:

$x = \frac{-18}{15}$

Therefore, the solution to the equation is $x = -\frac{18}{15}$ .

Final Answer

$-\frac{18}{15}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiplication: Multiply each numerator by the opposite denominator
Distribution: $6(3-x) = 18-6x$ and $9(4+x) = 36+9x$
Verification: Substitute $x = -\frac{18}{15}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Incorrectly distributing negative signs
Don't write 6(3-x) as 18-6x then forget the negative becomes positive when moving terms = wrong signs throughout! This creates calculation errors and wrong final answers. Always track negative signs carefully when distributing and moving terms across the equals sign.

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 can I cross-multiply these fractions?

Cross-multiplication works because you have one fraction equals another fraction. When $\frac{a}{b} = \frac{c}{d}$ , multiplying both sides by bd gives you $ad = bc$ !

Should I simplify the fraction -18/15?

Yes! Always simplify fractions to lowest terms. Since $\gcd(18,15) = 3$ , we get $-\frac{18}{15} = -\frac{6}{5}$ . Both forms are correct, but simplified is preferred.

What if I get confused with the signs when distributing?

Take it step by step! For $6(3-x)$ : multiply 6×3=18, then 6×(-x)=-6x. Write it as 18-6x, not 18+6x.

How do I check if x = -18/15 is correct?

Substitute back: $\frac{3-(-\frac{18}{15})}{9}$ should equal $\frac{4+(-\frac{18}{15})}{6}$ . If both sides give the same decimal value, you're right!

Can I solve this by clearing fractions instead?

Absolutely! Multiply everything by the LCD of 18: $18 \cdot \frac{3-x}{9} = 18 \cdot \frac{4+x}{6}$ gives $2(3-x) = 3(4+x)$ . Same answer, different method!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve for X in (3-x)/9 = (4+x)/6: Fraction Equation Practice

Cross-Multiplication with Algebraic Fractions

❤️ 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 can I cross-multiply these fractions?

Should I simplify the fraction -18/15?

What if I get confused with the signs when distributing?

How do I check if x = -18/15 is correct?

Can I solve this by clearing fractions instead?

🌟 Unlock Your Math Potential

More Questions

Solving Equations Using All Methods

Solve for X: Fraction Equation 4/(x+5) = 8/((2-x)×3)

Solve the Fraction Equation: Finding X in (6-x)/7 = 3(x-8)/9

Solve the Fraction Equation: 9/(x+5) = 11/(2-x)

Solve for X: Finding the Value in 9/x = 3/(x+2)

Simplifying and Combining Like Terms

Solve the Rational Equation: (5+3(x-2))/(5+x) = 3/4

Solve for X: Simplifying (6-3(x+4))/5 = (x-3)/2

Solve for X: Finding the Value in (9-x)/5 = x/4

Solve the Rational Equation: Finding X in (6+x)/(x+5) = 4/11