Solve for X: Finding X in -1/4x + 3 = 1/2 Linear Equation

Q: Why do we subtract 3 first instead of dealing with the fraction?

It's easier to isolate the variable term first! By subtracting 3 from both sides, we get $ -\frac{1}{4}x = -\frac{5}{2} $, making it simpler to solve.

Q: How do I multiply by -4 when I have a fraction?

Remember that multiplying by -4 is the same as dividing by $ -\frac{1}{4} $. So $ -\frac{5}{2} \times (-4) = \frac{5 \times 4}{2} = \frac{20}{2} = 10 $.

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

Track each step carefully! We have $ -\frac{1}{4}x = -\frac{5}{2} $. Multiplying both sides by -4 gives us: negative × negative = positive, so x = 10.

Q: Can I convert everything to decimals instead?

Yes, but fractions are often more accurate! Converting $ -\frac{1}{4} $ to -0.25 works, but keeping fractions avoids rounding errors in more complex problems.

Q: How do I check if x = 10 is really correct?

Substitute back: $ -\frac{1}{4}(10) + 3 = -2.5 + 3 = 0.5 = \frac{1}{2} $ ✓. Both sides equal $ \frac{1}{2} $, so our answer is right!

Linear Equations with Fractional Coefficients

Solve for X:

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

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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

00:19 Simplify what we can

00:29 Multiply by the denominator to eliminate the fraction

00:43 Simplify what we can

00:56 Negative times negative always equals positive

00:59 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:

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

Step-by-step solution

Let's solve the equation $-\frac{1}{4}x + 3 = \frac{1}{2}$ following these steps:

Step 1: Subtract 3 from both sides to eliminate the constant on the left.

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

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

Simplifying the right side gives:

$-\frac{1}{4}x = -\frac{5}{2}$

Step 2: Multiply both sides by $-4$ to isolate $x$ .

$x = -\frac{5}{2} \times (-4)$

$x = \frac{20}{2}$

$x = 10$

Thus, we find the solution to be $x = 10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Isolation Strategy: Subtract constants first, then eliminate fractional coefficients
Technique: Multiply by -4 to cancel $-\frac{1}{4}$ coefficient
Verification: Substitute x = 10: $-\frac{1}{4}(10) + 3 = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change signs when multiplying by negative
Don't multiply $-\frac{5}{2} \times (-4)$ and get -20! Negative times negative equals positive. Always remember that multiplying by a negative number flips the sign, giving you +20, so x = 10.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

Why do we subtract 3 first instead of dealing with the fraction?

It's easier to isolate the variable term first! By subtracting 3 from both sides, we get $-\frac{1}{4}x = -\frac{5}{2}$ , making it simpler to solve.

How do I multiply by -4 when I have a fraction?

Remember that multiplying by -4 is the same as dividing by $-\frac{1}{4}$ . So $-\frac{5}{2} \times (-4) = \frac{5 \times 4}{2} = \frac{20}{2} = 10$ .

What if I get confused with the negative signs?

Track each step carefully! We have $-\frac{1}{4}x = -\frac{5}{2}$ . Multiplying both sides by -4 gives us: negative × negative = positive, so x = 10.

Can I convert everything to decimals instead?

Yes, but fractions are often more accurate! Converting $-\frac{1}{4}$ to -0.25 works, but keeping fractions avoids rounding errors in more complex problems.

How do I check if x = 10 is really correct?

Substitute back: $-\frac{1}{4}(10) + 3 = -2.5 + 3 = 0.5 = \frac{1}{2}$ ✓. Both sides equal $\frac{1}{2}$ , so our answer is right!

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