Solve the Equation: Determining X in -2(4-3x)+4(2x-4)=8(2-x)

Q: Why do I keep getting the wrong sign when distributing?

When you see -2(4-3x), remember that the negative distributes to both terms: -2×4 = -8 and -2×(-3x) = +6x. The key is that negative times negative equals positive!

Q: How do I combine like terms correctly?

Look for terms with the same variable. In this problem, 6x and 8x are like terms (both have x), while -8 and -16 are constants. Combine separately: 6x + 8x = 14x and -8 - 16 = -24.

Q: What's the best way to check my fractional answer?

Substitute $ x = \frac{20}{11} $ back into the original equation. Calculate each side separately and verify they're equal. Use a calculator if needed - both sides should give you the same decimal value!

Q: Why is my final answer a fraction instead of a whole number?

That's completely normal! Many linear equations have fractional solutions. The answer $ \frac{20}{11} $ is already in simplest form since 20 and 11 share no common factors.

Q: Can I solve this without distributing first?

While you could try other approaches, distributing first is the most reliable method. It eliminates parentheses early, making it easier to see and combine like terms without confusion.

Linear Equations with Distribution and Fractions

Solve for X:

$-2(4-3x)+4(2x-4)=8(2-x)$

❤️ 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

00:04 Open parentheses properly, multiply by each factor

00:26 Collect like terms

00:40 Arrange the equation so that X is isolated on one side

00:56 Collect like terms

01:03 Isolate X

01:10 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:

$-2(4-3x)+4(2x-4)=8(2-x)$

Step-by-step solution

To solve this problem, let's break it down step-by-step:

Step 1: Expand the equation using the distributive property.

Apply the distributive property to each term: $-2(4 - 3x) + 4(2x - 4) = 8(2 - x)$ $-2 \cdot 4 + (-2) \cdot (-3x) + 4 \cdot 2x - 4 \cdot 4 = 8 \cdot 2 - 8 \cdot x$ which simplifies to:

$-8 + 6x + 8x - 16 = 16 - 8x$

Step 2: Gather like terms.

Combine $x$ terms and constants separately: $6x + 8x = 14x \quad \text{and} \quad -8 - 16 = -24$ Thus, the equation becomes: $14x - 24 = 16 - 8x$

Step 3: Isolate $x$ on one side.

Start by adding $8x$ to both sides to bring all terms involving $x$ to one side: $14x + 8x - 24 = 16$ which simplifies to: $22x - 24 = 16$

Step 4: Solve for $x$ .

Add 24 to both sides to isolate the term with $x$ : $22x = 16 + 24$ $22x = 40$ Finally, divide both sides by 22: $x = \frac{40}{22} = \frac{20}{11}$

Therefore, the solution to the equation is $\frac{20}{11}$ .

Final Answer

$\frac{20}{11}$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply distributive property to all terms inside parentheses
Technique: Combine like terms: 6x + 8x = 14x on left side
Check: Substitute $x = \frac{20}{11}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Sign errors when distributing negative coefficients
Don't forget that -2(4-3x) = -8 + 6x, not -8 - 6x! Students often lose track of negative signs during distribution, leading to wrong coefficients. Always distribute the negative sign carefully to each term inside parentheses.

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 keep getting the wrong sign when distributing?

When you see -2(4-3x), remember that the negative distributes to both terms: -2×4 = -8 and -2×(-3x) = +6x. The key is that negative times negative equals positive!

How do I combine like terms correctly?

Look for terms with the same variable. In this problem, 6x and 8x are like terms (both have x), while -8 and -16 are constants. Combine separately: 6x + 8x = 14x and -8 - 16 = -24.

What's the best way to check my fractional answer?

Substitute $x = \frac{20}{11}$ back into the original equation. Calculate each side separately and verify they're equal. Use a calculator if needed - both sides should give you the same decimal value!

Why is my final answer a fraction instead of a whole number?

That's completely normal! Many linear equations have fractional solutions. The answer $\frac{20}{11}$ is already in simplest form since 20 and 11 share no common factors.

Can I solve this without distributing first?

While you could try other approaches, distributing first is the most reliable method. It eliminates parentheses early, making it easier to see and combine like terms without confusion.

🌟 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