Solve for X in the Linear Equation: 2(4-x)=8

Q: Why can't I just divide both sides by 2 first?

You can't divide when there are parentheses with subtraction inside! Division doesn't work the same way as the distributive property. You must use distribution first, then solve the resulting equation.

Q: What if I get confused about which operation to do first?

Follow the order of operations: Handle parentheses first by distributing, then combine like terms, then isolate the variable. Write out each step clearly!

Q: How do I know when to use the distributive property?

Use it whenever you see a number outside parentheses like $ 2(4-x) $ or $ -3(x+5) $. The distributive property helps you eliminate the parentheses.

Q: What does it mean when x equals 0?

$ x = 0 $ is a perfectly valid answer! It means when you substitute 0 for x in the original equation, both sides become equal. Zero is a real number just like any other solution.

Q: Can I check my answer a different way?

Yes! Besides substitution, you can work backwards: Start with your answer $ x = 0 $, plug it into $ 4-x = 4-0 = 4 $, then $ 2(4) = 8 $ ✓

Linear Equations with Distributive Property

Solve for x:

$2(4-x)=8$

❤️ 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 Determine X

00:04 Open the brackets by multiplying by each factor

00:13 Arrange the equation so that the unknown X is only on one side

00:21 Collect like terms

00:26 Isolate X

00:32 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$2(4-x)=8$

Step-by-step solution

To solve this equation, follow these steps:

Step 1: Apply the distributive property to the equation:

$2(4-x) = 2 \times 4 - 2 \times x = 8 - 2x$
Step 2: Simplify the equation:

The equation now becomes: $8 - 2x = 8$
Step 3: Isolate the variable $x$ by simplifying the equation:

First, subtract 8 from both sides:
$8 - 2x - 8 = 8 - 8$
This simplifies to:
$-2x = 0$
Step 4: Solve for $x$ by dividing both sides by -2:

$x = \frac{0}{-2} = 0$

Therefore, the solution to the equation is $x = 0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply outside number by each term inside parentheses
Technique: $2(4-x) = 8-2x$ then subtract 8 from both sides
Check: Substitute x = 0: $2(4-0) = 2(4) = 8$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't just multiply 2 × 4 = 8 and ignore the x term! This gives you 8 = 8 which seems right but misses the -2x completely. Always distribute the outside number to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=0 $$

FAQ

Everything you need to know about this question

Why can't I just divide both sides by 2 first?

You can't divide when there are parentheses with subtraction inside! Division doesn't work the same way as the distributive property. You must use distribution first, then solve the resulting equation.

What if I get confused about which operation to do first?

Follow the order of operations: Handle parentheses first by distributing, then combine like terms, then isolate the variable. Write out each step clearly!

How do I know when to use the distributive property?

Use it whenever you see a number outside parentheses like $2(4-x)$ or $-3(x+5)$ . The distributive property helps you eliminate the parentheses.

What does it mean when x equals 0?

$x = 0$ is a perfectly valid answer! It means when you substitute 0 for x in the original equation, both sides become equal. Zero is a real number just like any other solution.

Can I check my answer a different way?

Yes! Besides substitution, you can work backwards: Start with your answer $x = 0$ , plug it into $4-x = 4-0 = 4$ , then $2(4) = 8$ ✓

🌟 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