Solve the Linear Equation: 5(X-8) + 1/2 = 0

Q: Why do I need to distribute 5 to both x and -8?

The distributive property requires you to multiply the outside number by every term inside the parentheses. So $ 5(x - 8) $ becomes $ 5x - 40 $, not just $ 5x - 8 $!

Q: How do I combine -40 and 1/2?

Convert both to the same denominator! Change -40 to $ -\frac{80}{2} $, then combine: $ -\frac{80}{2} + \frac{1}{2} = -\frac{79}{2} $. This keeps everything as fractions for easier calculation.

Q: Why is my final answer a fraction?

That's completely normal! Linear equations often have fractional solutions. $ x = \frac{79}{10} $ is the exact answer, which equals 7.9 as a decimal.

Q: How do I divide by 5 when I have a fraction?

Dividing by 5 is the same as multiplying by $ \frac{1}{5} $. So $ \frac{79}{2} ÷ 5 = \frac{79}{2} × \frac{1}{5} = \frac{79}{10} $.

Q: Can I check my answer without substituting back?

Always substitute back! It's the most reliable way to catch errors. Plug $ x = \frac{79}{10} $ into the original equation and verify both sides equal zero.

Q: What if I get confused with all the fraction operations?

Take it one step at a time! First distribute, then combine like terms, then isolate x. Draw clear fraction bars and double-check your arithmetic at each step.

Linear Equations with Distribution and Fractions

Solve for X:

$5(x-8)+\frac{1}{2}=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Open brackets properly, multiply by each factor

00:20 Arrange the equation so that only the unknown X is on one side

00:28 Isolate X

00:41 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:

$5(x-8)+\frac{1}{2}=0$

Step-by-step solution

To solve the linear equation $5(x-8)+\frac{1}{2}=0$ , follow these steps:

Step 1: Distribute the 5 across $(x-8)$ .

The equation becomes:

$5x - 40 + \frac{1}{2} = 0$ .

Step 2: Combine the constants on the left side.

Combine $-40$ and $\frac{1}{2}$ :

$5x - 40 + \frac{1}{2} = 0$ .

Convert $-40$ into a fraction to simplify: $-40 = -\frac{80}{2}$ .

The equation becomes:

$5x - \frac{80}{2} + \frac{1}{2} = 0$ .

Simplify it to:

$5x - \frac{79}{2} = 0$ .

Step 3: Isolate $x$ .

To move $-\frac{79}{2}$ to the other side, we add $\frac{79}{2}$ to both sides:

$5x = \frac{79}{2}$ .

Step 4: Solve for $x$ .

Divide both sides by 5 to isolate $x$ :

$x = \frac{79}{2} \div 5$ .

$x = \frac{79}{2} \times \frac{1}{5}$ .

$x = \frac{79}{10}$ .

Therefore, the solution to the equation is $x = \frac{79}{10}$ .

Final Answer

$\frac{79}{10}$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply multiplication to every term inside parentheses first
Fraction Technique: Convert -40 to $-\frac{80}{2}$ when combining with $\frac{1}{2}$
Check Solution: Substitute $x = \frac{79}{10}$ back: $5(\frac{79}{10} - 8) + \frac{1}{2} = 0$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the coefficient to all terms in parentheses
Don't multiply 5 by just x and forget the -8 = wrong equation setup! This creates 5x - 8 instead of 5x - 40, leading to completely wrong answers. Always distribute the coefficient to every single 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 do I need to distribute 5 to both x and -8?

The distributive property requires you to multiply the outside number by every term inside the parentheses. So $5(x - 8)$ becomes $5x - 40$ , not just $5x - 8$ !

How do I combine -40 and 1/2?

Convert both to the same denominator! Change -40 to $-\frac{80}{2}$ , then combine: $-\frac{80}{2} + \frac{1}{2} = -\frac{79}{2}$ . This keeps everything as fractions for easier calculation.

Why is my final answer a fraction?

That's completely normal! Linear equations often have fractional solutions. $x = \frac{79}{10}$ is the exact answer, which equals 7.9 as a decimal.

How do I divide by 5 when I have a fraction?

Dividing by 5 is the same as multiplying by $\frac{1}{5}$ . So $\frac{79}{2} ÷ 5 = \frac{79}{2} × \frac{1}{5} = \frac{79}{10}$ .

Can I check my answer without substituting back?

Always substitute back! It's the most reliable way to catch errors. Plug $x = \frac{79}{10}$ into the original equation and verify both sides equal zero.

What if I get confused with all the fraction operations?

Take it one step at a time! First distribute, then combine like terms, then isolate x. Draw clear fraction bars and double-check your arithmetic at each step.

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