Solve for X: (2x-4)×(1/8) = 4 Linear Equation

Q: Why do I multiply by 8 instead of dividing by 1/8?

Great question! Multiplying by 8 and dividing by $ \frac{1}{8} $ give the same result, but multiplication is much easier to calculate and less prone to errors.

Q: What if I forget to multiply both sides by 8?

If you only multiply one side, you'll break the equality! The equation won't balance anymore. Always remember: whatever you do to one side, you must do to the other side too.

Q: How do I know what number to multiply by?

Look at the fraction's denominator! Since we have $ \frac{1}{8} $, multiply both sides by 8 (the reciprocal). This will cancel out the fraction completely.

Q: Can I solve this equation a different way?

Yes! You could also distribute first: $ 4 = \frac{2x}{8} - \frac{4}{8} $, then simplify to $ 4 = \frac{x}{4} - \frac{1}{2} $. But multiplying by 8 first is usually faster!

Q: What if I get a different answer when checking?

Go back and check your arithmetic! Common errors include: forgetting to multiply both terms by 8, or making calculation mistakes. The correct answer should always satisfy the original equation.

Linear Equations with Fractional Multiplication

$4=(2x-4)\times\frac{1}{8}$

How much is X worth?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem together!

00:09 First, multiply by the denominator to remove the fraction. Multiply carefully!

00:16 Next, open the parentheses. Multiply each term inside.

00:23 Now, rearrange the equation so that only the unknown X is on one side.

00:32 Then, collect like terms to simplify.

00:35 Isolate X by performing the inverse operations.

00:42 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$4=(2x-4)\times\frac{1}{8}$

How much is X worth?

Step-by-step solution

To solve this problem, we'll proceed with these steps:

Step 1: Eliminate the fraction by multiplying both sides of the equation by 8.
Step 2: Simplify the resulting equation.
Step 3: Solve for $x$ .

Let's work through each step:

Step 1: Multiply both sides of the equation by 8 to eliminate the fraction:

4 \times 8 = (2x - 4) \times \frac{1}{8} \times 8

This simplifies to:

32 = 2x - 4

Step 2: Isolate $2x$ by adding 4 to both sides:

32 + 4 = 2x

36 = 2x

Step 3: Solve for $x$ by dividing both sides by 2:

\frac{36}{2} = x

18 = x

Therefore, the solution to the problem is: $x = 18$ .

Comparing this with the given choices, the correct choice is:

Choice 3: $(18)$

Final Answer

$18$

Key Points to Remember

Essential concepts to master this topic

Elimination Rule: Multiply both sides by reciprocal to clear fractions
Technique: Multiply by 8 to get $32 = 2x - 4$
Check: Substitute x = 18: $(2(18) - 4) \times \frac{1}{8} = 4$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by the fraction instead of multiplying by reciprocal
Don't divide both sides by 1/8 and get confused = makes calculation harder! Division by a fraction is the same as multiplication by its reciprocal, but students often make arithmetic errors. Always multiply both sides by 8 to eliminate the fraction cleanly.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do I multiply by 8 instead of dividing by 1/8?

Great question! Multiplying by 8 and dividing by $\frac{1}{8}$ give the same result, but multiplication is much easier to calculate and less prone to errors.

What if I forget to multiply both sides by 8?

If you only multiply one side, you'll break the equality! The equation won't balance anymore. Always remember: whatever you do to one side, you must do to the other side too.

How do I know what number to multiply by?

Look at the fraction's denominator! Since we have $\frac{1}{8}$ , multiply both sides by 8 (the reciprocal). This will cancel out the fraction completely.

Can I solve this equation a different way?

Yes! You could also distribute first: $4 = \frac{2x}{8} - \frac{4}{8}$ , then simplify to $4 = \frac{x}{4} - \frac{1}{2}$ . But multiplying by 8 first is usually faster!

What if I get a different answer when checking?

Go back and check your arithmetic! Common errors include: forgetting to multiply both terms by 8, or making calculation mistakes. The correct answer should always satisfy the original equation.

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