Solve the Fraction Equation: Isolate X in -1/4(x-2)=3

Q: Why do I multiply by -4 instead of 4?

You multiply by -4 because it's the reciprocal of $ -\frac{1}{4} $. This completely eliminates the fraction in one step: $ (-4) \times (-\frac{1}{4}) = 1 $.

Q: What if I multiply by positive 4 instead?

If you multiply by +4, you get $ -(x-2) = 12 $, which still works but requires an extra step to handle the negative sign. Using -4 is more efficient.

Q: How do I handle the parentheses after clearing the fraction?

Once you get $ (x-2) = -12 $, simply add 2 to both sides: $ x = -12 + 2 = -10 $. The parentheses become unnecessary.

Q: Why is the answer negative?

The answer is negative because we started with a negative coefficient $ -\frac{1}{4} $ and a positive result (3). This combination naturally leads to a negative value for x.

Q: Can I distribute the fraction first instead?

Yes! You could distribute: $ -\frac{1}{4}x + \frac{1}{2} = 3 $, then solve. However, multiplying by -4 first is usually easier because it avoids working with multiple fractions.

Linear Equations with Negative Fractional Coefficients

Solve for X:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Multiply by (-4) to eliminate the fraction

00:17 Arrange the equation so that one side has only the unknown X

00:23 Collect like terms

00:27 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:

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

Step-by-step solution

To solve this problem, we will proceed with the following steps:

Step 1: Start with the given equation: $-\frac{1}{4}(x-2)=3$ .
Step 2: Multiply both sides by -4 to eliminate the fraction: $(-4) \times -\frac{1}{4}(x-2) = (-4) \times 3$ .
Step 3: Simplify: $(x-2) = -12$ .
Step 4: Solve for $x$ by adding 2 to both sides: $x = -12 + 2$ .
Step 5: Simplify to find the value of $x$ : $x = -10$ .

Therefore, the solution to the equation is $x = -10$ .

According to the multiple-choice options, the correct answer is choice 2: -10.

Final Answer

-10

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by reciprocal to eliminate fractions
Technique: Multiply by -4 to clear $-\frac{1}{4}$ : (-4) × 3 = -12
Check: Substitute x = -10: $-\frac{1}{4}(-10-2) = -\frac{1}{4}(-12) = 3$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply both sides by the same value
Don't multiply only the left side by -4 and leave the right side as 3 = wrong answer of x = -14! This breaks the equation's balance. Always multiply both sides by the same number to maintain equality.

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 multiply by -4 instead of 4?

You multiply by -4 because it's the reciprocal of $-\frac{1}{4}$ . This completely eliminates the fraction in one step: $(-4) \times (-\frac{1}{4}) = 1$ .

What if I multiply by positive 4 instead?

If you multiply by +4, you get $-(x-2) = 12$ , which still works but requires an extra step to handle the negative sign. Using -4 is more efficient.

How do I handle the parentheses after clearing the fraction?

Once you get $(x-2) = -12$ , simply add 2 to both sides: $x = -12 + 2 = -10$ . The parentheses become unnecessary.

Why is the answer negative?

The answer is negative because we started with a negative coefficient $-\frac{1}{4}$ and a positive result (3). This combination naturally leads to a negative value for x.

Can I distribute the fraction first instead?

Yes! You could distribute: $-\frac{1}{4}x + \frac{1}{2} = 3$ , then solve. However, multiplying by -4 first is usually easier because it avoids working with multiple fractions.

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