Solve for X: -x + 3(x-4) = 5 - 1/2x Linear Equation

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

You must distribute first because parentheses create a single unit. Moving terms before distributing changes the equation's meaning and leads to wrong answers!

Q: How do I add 2x and 1/2x together?

Convert to the same denominator: $ 2x = \frac{4}{2}x $, so $ \frac{4}{2}x + \frac{1}{2}x = \frac{5}{2}x $. Always find a common denominator when adding fractions!

Q: Can I multiply everything by 2 to clear the fraction?

Yes! Multiplying both sides by 2 eliminates $ \frac{1}{2}x $ and makes calculations easier. Just remember to multiply every single term on both sides.

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

Not all equations have whole number solutions! $ x = \frac{34}{5} $ is perfectly correct. You can convert to decimal (6.8) or mixed number (6⅘) if needed.

Q: How do I check if 34/5 is really correct?

Substitute back into the original equation: $ -\frac{34}{5} + 3(\frac{34}{5} - 4) = 5 - \frac{1}{2} \cdot \frac{34}{5} $. Both sides should equal 5 when simplified!

Linear Equations with Mixed Fraction Terms

Solve for x:

$-x+3(x-4)=5-\frac{1}{2}x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 Open brackets properly, multiply by each factor

00:16 Collect like terms

00:26 Arrange the equation so that X is isolated on one side

00:46 Collect like terms

00:53 Convert from mixed number to fraction

00:57 Multiply by the reciprocal to isolate X

01:13 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:

$-x+3(x-4)=5-\frac{1}{2}x$

Step-by-step solution

To solve the equation $-x + 3(x-4) = 5 - \frac{1}{2}x$ , follow these steps:

**Step 1**: Distribute the $3$ on the left side:
$-x + 3x - 12 = 5 - \frac{1}{2}x$ .
**Step 2**: Combine like terms on the left:
$(2x - 12) = 5 - \frac{1}{2}x$ .
**Step 3**: Add $\frac{1}{2}x$ to both sides to get only the variable terms on one side:
$2x + \frac{1}{2}x - 12 = 5$ .
**Step 4**: Simplify by combining the $x$ terms:
$\frac{5}{2}x - 12 = 5$ .
**Step 5**: Add 12 to both sides to isolate terms with $x$ :
$\frac{5}{2}x = 17$ .
**Step 6**: Multiply both sides by $\frac{2}{5}$ to solve for $x$ :
$x = 17 \times \frac{2}{5} = \frac{34}{5}$ .

Therefore, the solution to the problem is $x = \frac{34}{5}$ .

Final Answer

$\frac{34}{5}$

Key Points to Remember

Essential concepts to master this topic

Distribution: Apply distributive property before combining like terms
Technique: Convert $2x + \frac{1}{2}x$ to $\frac{5}{2}x$ by finding common denominator
Check: Substitute $x = \frac{34}{5}$ back: both sides equal 5 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the 3 to both terms inside parentheses
Don't just multiply 3(x) and ignore the -4 = missing -12 term! This creates an incomplete equation and wrong final answer. Always distribute to every term: 3(x-4) = 3x - 12.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

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

You must distribute first because parentheses create a single unit. Moving terms before distributing changes the equation's meaning and leads to wrong answers!

How do I add 2x and 1/2x together?

Convert to the same denominator: $2x = \frac{4}{2}x$ , so $\frac{4}{2}x + \frac{1}{2}x = \frac{5}{2}x$ . Always find a common denominator when adding fractions!

Can I multiply everything by 2 to clear the fraction?

Yes! Multiplying both sides by 2 eliminates $\frac{1}{2}x$ and makes calculations easier. Just remember to multiply every single term on both sides.

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

Not all equations have whole number solutions! $x = \frac{34}{5}$ is perfectly correct. You can convert to decimal (6.8) or mixed number (6⅘) if needed.

How do I check if 34/5 is really correct?

Substitute back into the original equation: $-\frac{34}{5} + 3(\frac{34}{5} - 4) = 5 - \frac{1}{2} \cdot \frac{34}{5}$ . Both sides should equal 5 when simplified!

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