Solve the Complex Equation: 130÷(10/2x)-(23x-204)

Q: Why do I flip the fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal. When you have $ a \div \frac{b}{c} $, it becomes $ a \times \frac{c}{b} $. This is a fundamental rule!

Q: How do I simplify fractions with variables in the denominator?

First reduce any numbers in the fraction. For $ \frac{10}{2x} $, divide both numerator and denominator by 2 to get $ \frac{5}{x} $.

Q: What's the difference between : and ÷ symbols?

Both symbols mean division - they're exactly the same! The colon (:) is commonly used in some countries, while ÷ is used in others. Both represent the same operation.

Q: How do I handle negative signs in parentheses?

When you have a negative sign before parentheses like $ -(23x - 204) $, distribute it to every term inside: $ -23x + 204 $.

Q: Can I check my answer with any value of x?

Yes! Pick any simple value like x = 1 or x = 2, substitute it into both the original expression and your answer. If they give the same result, you're correct!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Division is also multiplication by the reciprocal

00:12 Negative times positive is always negative

00:16 Negative times negative is always positive

00:24 Let's factor 130 into factors 10 and 13

00:36 Let's reduce what we can

00:47 Let's group factors

00:52 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$130:\frac{10}{2x}-(23x-204)=\text{?}$

2

Step-by-step solution

To solve the given expression $130 : \frac{10}{2x} - (23x - 204)$ , follow these steps:

Firstly, simplify the fraction $\frac{10}{2x}$ to get $\frac{5}{x}$ .
Next, perform the division $130 \div \frac{5}{x}$ . This is equivalent to multiplying $130$ by the reciprocal, resulting in $130 \times \frac{x}{5}$ . Simplify this to get $26x$ .
The expression now becomes $26x - (23x - 204)$ .
Distribute the negative sign inside the parentheses to get $26x - 23x + 204$ .
Simplify by combining like terms, which yields $3x + 204$ .

Therefore, the solution to the problem is $3x + 204$ . This matches option 1 from our choices, confirming it as the correct answer.

3

Final Answer

$3x+204$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Dividing by a fraction means multiply by reciprocal
Technique: $130 \div \frac{5}{x} = 130 \times \frac{x}{5} = 26x$
Check: Substitute x=1: 26(1) - (23(1) - 204) = 207 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly handling division by fractions
Don't divide 130 directly by the numerator and denominator separately = completely wrong result! This ignores the fundamental rule of fraction division. Always convert division by a fraction into multiplication by its reciprocal.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why do I flip the fraction when dividing?

+

Dividing by a fraction is the same as multiplying by its reciprocal. When you have $a \div \frac{b}{c}$ , it becomes $a \times \frac{c}{b}$ . This is a fundamental rule!

How do I simplify fractions with variables in the denominator?

+

First reduce any numbers in the fraction. For $\frac{10}{2x}$ , divide both numerator and denominator by 2 to get $\frac{5}{x}$ .

What's the difference between : and ÷ symbols?

+

Both symbols mean division - they're exactly the same! The colon (:) is commonly used in some countries, while ÷ is used in others. Both represent the same operation.

How do I handle negative signs in parentheses?

+

When you have a negative sign before parentheses like $-(23x - 204)$ , distribute it to every term inside: $-23x + 204$ .

Can I check my answer with any value of x?

+

Yes! Pick any simple value like x = 1 or x = 2, substitute it into both the original expression and your answer. If they give the same result, you're correct!

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Solve the Complex Equation: 130÷(10/2x)-(23x-204)

Order of Operations with Complex Division

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