Solve for X: -1/4 + x = -1/2x Linear Equation Challenge

Q: Why do I need to add fractions when combining x terms?

When you have $ x + \frac{1}{2}x $, think of it as $ \frac{2}{2}x + \frac{1}{2}x $. Just like adding regular fractions, you need a common denominator to combine them properly!

Q: Can I multiply everything by 4 to clear the fractions?

Yes! Multiplying by 4 gives you $ -1 + 4x = -2x $, which is easier to work with. This is a great strategy when dealing with fractional coefficients.

Q: What if I get confused with the fraction arithmetic?

Write out each step carefully! Convert $ x $ to $ \frac{2}{2}x $ first, then add: $ \frac{2}{2}x + \frac{1}{2}x = \frac{3}{2}x $. Take your time with fraction operations.

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

Many linear equations have fractional solutions! This is completely normal. Always simplify your fraction to lowest terms and double-check by substituting back into the original equation.

Linear Equations with Fractional Terms

Solve for X:

$-\frac{1}{4}+x=-\frac{1}{2}x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Isolate the unknown X

00:14 Simplify what's possible

00:31 Continue to isolate the unknown X

00:47 Negative times negative always equals positive

00:56 Be careful to multiply numerator by numerator and denominator by denominator

00:59 Simplify what's possible

01:05 Factor 12 into 6 and 2

01:11 Simplify what's possible

01:16 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$-\frac{1}{4}+x=-\frac{1}{2}x$

Step-by-step solution

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

Step 1: Begin by moving the terms involving $x$ to one side of the equation. We can do this by adding $\frac{1}{2}x$ to both sides. This gives:
$-\frac{1}{4} + x + \frac{1}{2}x = 0$
Step 2: Recognize that $x + \frac{1}{2}x$ can be combined into a single term:\br $-\frac{1}{4} + \frac{3}{2}x = 0$
Step 3: Isolate $\frac{3}{2}x$ by adding $\frac{1}{4}$ to both sides, resulting in:
$\frac{3}{2}x = \frac{1}{4}$
Step 4: Solve for $x$ by multiplying both sides by $\frac{2}{3}$ , which is the reciprocal of $\frac{3}{2}$ :
$x = \frac{1}{4} \cdot \frac{2}{3}$
Step 5: Simplify the multiplication on the right side:
$x = \frac{2}{12} = \frac{1}{6}$

Thus, the solution to the equation is $x = \frac{1}{6}$ .

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Collection: Move all x terms to one side first
Technique: $x + \frac{1}{2}x = \frac{3}{2}x$ by finding common denominator
Check: Substitute $\frac{1}{6}$ : $-\frac{1}{4} + \frac{1}{6} = -\frac{1}{12}$ and $-\frac{1}{2} \cdot \frac{1}{6} = -\frac{1}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms correctly
Don't write $x + \frac{1}{2}x = \frac{1}{2}x$ = wrong coefficient! This ignores the whole x term and gives $x = \frac{1}{2}$ instead of $\frac{1}{6}$ . Always convert to common denominators: $\frac{2}{2}x + \frac{1}{2}x = \frac{3}{2}x$ .

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to add fractions when combining x terms?

When you have $x + \frac{1}{2}x$ , think of it as $\frac{2}{2}x + \frac{1}{2}x$ . Just like adding regular fractions, you need a common denominator to combine them properly!

Can I multiply everything by 4 to clear the fractions?

Yes! Multiplying by 4 gives you $-1 + 4x = -2x$ , which is easier to work with. This is a great strategy when dealing with fractional coefficients.

How do I know which side to move the x terms to?

It doesn't matter! You can move all x terms to either side. Choose whichever gives you a positive coefficient for x to avoid working with negatives.

What if I get confused with the fraction arithmetic?

Write out each step carefully! Convert $x$ to $\frac{2}{2}x$ first, then add: $\frac{2}{2}x + \frac{1}{2}x = \frac{3}{2}x$ . Take your time with fraction operations.

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

Many linear equations have fractional solutions! This is completely normal. Always simplify your fraction to lowest terms and double-check by substituting back into the original equation.

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