Solve the Fraction Equation: Discovering X in -1/2(x + 1/4) = 1/8

Q: How do I distribute -4 to both terms?

Multiply each term inside the parentheses: -4 × x = -4x and -4 × 1/4 = -1. So $ -4(x + \frac{1}{4}) = -4x - 1 $.

Q: What if I get confused with the negative signs?

Take it one step at a time! When you see a negative coefficient like -4, remember it affects everything inside the parentheses. Write out each multiplication separately to avoid errors.

Q: Why is my answer negative?

Negative answers are perfectly normal! In this problem, $ x = -\frac{1}{2} $ makes sense because we need a value that, when plugged back in, gives us the positive result $ \frac{1}{8} $.

Q: How can I check if -1/2 is really correct?

Substitute back: $ -\frac{1}{2}(-\frac{1}{2} + \frac{1}{4}) = -\frac{1}{2}(-\frac{1}{4}) = \frac{1}{8} $. Since both sides equal $ \frac{1}{8} $, your answer is correct!

Linear Equations with Fractional Distribution

Solve for X:

$-\frac{1}{2}(x+\frac{1}{4})=\frac{1}{8}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 Multiply by (-2) to eliminate the fraction

00:18 Factor 8 into factors 4 and 2

00:25 Simplify what's possible

00:30 Arrange the equation so that X is isolated on one side

00:47 Factor 4 into factors 2 and 2

00:51 Simplify what's possible

00:56 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:

$-\frac{1}{2}(x+\frac{1}{4})=\frac{1}{8}$

Step-by-step solution

To solve the equation $-\frac{1}{2}(x+\frac{1}{4})=\frac{1}{8}$ , we will first eliminate the fraction by multiplying both sides by the common denominator. The common denominator here is 8, so we proceed as follows:

Step 1: Multiply both sides by 8 to eliminate the fractions:
$8 \left(-\frac{1}{2}(x+\frac{1}{4})\right) = 8 \times \frac{1}{8}$
Step 2: Simplify the left side:
$-4(x+\frac{1}{4}) = 1$
Step 3: Distribute $-4$ into the terms inside the parentheses:
$-4x - 1 = 1$
Step 4: Add 1 to both sides to isolate the term with $x$ :
$-4x = 2$
Step 5: Divide both sides by $-4$ to solve for $x$ :
$x = \frac{2}{-4} = -\frac{1}{2}$

Therefore, the solution to the equation is $x = -\frac{1}{2}$ .

Final Answer

$-\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by common denominator to clear fractions
Technique: Distribute after clearing fractions: -4(x + 1/4) becomes -4x - 1
Check: Substitute x = -1/2: -1/2(-1/2 + 1/4) = 1/8 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute negative coefficient
Don't just multiply the first term by -4 and ignore the second term = -4x + 1/4 instead of -4x - 1! This gives a completely wrong equation. Always distribute the coefficient to every term inside the 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 multiply both sides by 8 first?

Multiplying by 8 (the LCD) clears all fractions in one step, making the problem much easier! Without this, you'd be working with messy fractions throughout the entire solution.

How do I distribute -4 to both terms?

Multiply each term inside the parentheses: -4 × x = -4x and -4 × 1/4 = -1. So $-4(x + \frac{1}{4}) = -4x - 1$ .

What if I get confused with the negative signs?

Take it one step at a time! When you see a negative coefficient like -4, remember it affects everything inside the parentheses. Write out each multiplication separately to avoid errors.

Why is my answer negative?

Negative answers are perfectly normal! In this problem, $x = -\frac{1}{2}$ makes sense because we need a value that, when plugged back in, gives us the positive result $\frac{1}{8}$ .

How can I check if -1/2 is really correct?

Substitute back: $-\frac{1}{2}(-\frac{1}{2} + \frac{1}{4}) = -\frac{1}{2}(-\frac{1}{4}) = \frac{1}{8}$ . Since both sides equal $\frac{1}{8}$ , your answer is correct!

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