Solve for X: Linear Equation 3-4(x-2)=6x+4(3-x)

Q: Why do I need to distribute first instead of just moving terms around?

You must eliminate parentheses first using the distributive property! You can't move terms that are still inside parentheses. Think of parentheses as containers - you need to unpack them before rearranging.

Q: How do I keep track of positive and negative signs when distributing?

Write out each step carefully! For $ -4(x-2) $, think: negative 4 times x equals negative 4x, and negative 4 times negative 2 equals positive 8. Take your time with signs!

Q: What's the easiest way to combine like terms after distributing?

Group similar terms together first. Circle all the x-terms on one side and all the constants on the other. This helps you see what to combine: $ 11 - 4x = 2x + 12 $ becomes clearer.

Q: Is there a faster way to solve this type of equation?

Accuracy is more important than speed! Follow the steps: distribute, combine like terms, isolate x. Once you master this process, you'll naturally get faster while avoiding mistakes.

Linear Equations with Distributive Property

Solve for X:

$3-4(x-2)=6x+4(3-x)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:06 Carefully open brackets properly, multiply by each factor

00:23 Solve each multiplication separately

00:28 Negative times negative always equals positive

00:38 Positive times negative always equals negative

00:47 Collect like terms

01:00 Arrange the equation so that X is isolated on one side

01:17 Collect like terms

01:28 Isolate X

01:42 Simplify as much as possible

01:47 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:

$3-4(x-2)=6x+4(3-x)$

Step-by-step solution

Let's solve the equation $3-4(x-2)=6x+4(3-x)$ .

First, apply the distributive property on both sides:

For the left side: $3 - 4(x - 2)$ becomes $3 - 4x + 8$ , which simplifies to $11 - 4x$ .
For the right side: $6x + 4(3 - x)$ becomes $6x + 12 - 4x$ , which simplifies to $2x + 12$ .

Now the equation is:

$11 - 4x = 2x + 12$

Combine like terms to isolate $x$ . First, move all terms containing $x$ to one side and constant terms to the other side:

Add $4x$ to both sides: $11 = 6x + 12$ .
Subtract 12 from both sides: $11 - 12 = 6x$ , which simplifies to $-1 = 6x$ .

Finally, solve for $x$ by dividing both sides by 6:

$x = -\frac{1}{6}$ .

Therefore, the solution to the problem is $x = -\frac{1}{6}$ , which corresponds to choice 4.

Final Answer

$-\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Apply to parentheses before combining like terms
Technique: $-4(x-2) = -4x + 8$ and $4(3-x) = 12 - 4x$
Check: Substitute $x = -\frac{1}{6}$ into original equation: both sides equal 11 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute negative signs properly
Don't just distribute the 4 in -4(x-2) and ignore the negative = wrong signs throughout! This creates incorrect terms like -4x - 8 instead of -4x + 8. Always distribute both the coefficient AND its sign to every term inside parentheses.

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 do I need to distribute first instead of just moving terms around?

You must eliminate parentheses first using the distributive property! You can't move terms that are still inside parentheses. Think of parentheses as containers - you need to unpack them before rearranging.

How do I keep track of positive and negative signs when distributing?

Write out each step carefully! For $-4(x-2)$ , think: negative 4 times x equals negative 4x, and negative 4 times negative 2 equals positive 8. Take your time with signs!

What's the easiest way to combine like terms after distributing?

Group similar terms together first. Circle all the x-terms on one side and all the constants on the other. This helps you see what to combine: $11 - 4x = 2x + 12$ becomes clearer.

Why did I get a negative fraction as my answer?

Negative fractions are completely normal solutions! In this problem, when we solve $-1 = 6x$ , dividing gives us $x = -\frac{1}{6}$ . Always check your work by substituting back.

Is there a faster way to solve this type of equation?

Accuracy is more important than speed! Follow the steps: distribute, combine like terms, isolate x. Once you master this process, you'll naturally get faster while avoiding mistakes.

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Solve for X: Linear Equation 3-4(x-2)=6x+4(3-x)

Linear Equations with Distributive Property

❤️ 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 need to distribute first instead of just moving terms around?

How do I keep track of positive and negative signs when distributing?

What's the easiest way to combine like terms after distributing?

Why did I get a negative fraction as my answer?

Is there a faster way to solve this type of equation?

🌟 Unlock Your Math Potential

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