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

Q: What if I distribute incorrectly?

Double-check each term! Remember: $ -3 \times \frac{1}{2}x = -\frac{3}{2}x $ and $ -3 \times 4 = -12 $. The negative sign affects everything.

Q: How do I handle the negative fraction answer?

Negative fractions are normal! $ -\frac{25}{3} $ means the same as $ \frac{-25}{3} $. Keep it as an improper fraction unless asked to convert.

Q: How do I verify my negative answer is correct?

Substitute $ x = -\frac{25}{3} $ into the original equation. If $ -3(\frac{1}{2} \cdot (-\frac{25}{3}) + 4) = \frac{1}{2} $, you're right!

Linear Equations with Distributive Property

Solve for x:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the unknown value of X together.

00:10 First, open the parentheses properly and multiply each term inside.

00:21 Next, multiply everything by 2 to get rid of any fractions.

00:36 Now, arrange the equation so that X is all by itself on one side.

00:44 Time to collect like terms.

00:48 Then, isolate X to find its value.

00:56 And just like that, we've solved the problem for X!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

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

Step-by-step solution

We open the parentheses on the left side by the distributive property and use the formula:

$a(x+b)=ax+ab$

$-\frac{3}{2}x-12=\frac{1}{2}$

We multiply all terms by 2 to get rid of the fractions:

$-3x-12\times2=1$

$-3x-24=1$

We will move the minus 24 to the right section and keep the corresponding sign:

$-3x=24+1$

$-3x=25$

Divide both sections by minus 3:

$\frac{-3x}{-3}=\frac{25}{-3}$

$x=-\frac{25}{3}$

Final Answer

$-\frac{25}{3}$

Key Points to Remember

Essential concepts to master this topic

Distributive Rule: Multiply -3 by each term inside parentheses first
Technique: Clear fractions by multiplying all terms by 2: $-3x - 24 = 1$
Check: Substitute $x = -\frac{25}{3}$ back into original equation to verify ✓

Common Mistakes

Avoid these frequent errors

Not distributing negative sign correctly
Don't forget the negative sign when distributing: -3(1/2x + 4) = -3/2x - 12, not -3/2x + 12! Missing the negative creates a completely wrong equation. Always distribute the negative sign to every term inside parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=1 $$

What is the value of x?

FAQ

Everything you need to know about this question

Why do I multiply by 2 to clear fractions?

Multiplying by 2 eliminates all denominators of 2 in one step! This turns $-\frac{3}{2}x - 12 = \frac{1}{2}$ into the simpler $-3x - 24 = 1$ .

What if I distribute incorrectly?

Double-check each term! Remember: $-3 \times \frac{1}{2}x = -\frac{3}{2}x$ and $-3 \times 4 = -12$ . The negative sign affects everything.

How do I handle the negative fraction answer?

Negative fractions are normal! $-\frac{25}{3}$ means the same as $\frac{-25}{3}$ . Keep it as an improper fraction unless asked to convert.

Can I solve this without clearing fractions first?

Yes, but it's much harder! You'd work with fractions throughout. Clearing fractions first makes the arithmetic much simpler and reduces calculation errors.

How do I verify my negative answer is correct?

Substitute $x = -\frac{25}{3}$ into the original equation. If $-3(\frac{1}{2} \cdot (-\frac{25}{3}) + 4) = \frac{1}{2}$ , you're right!

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