Solve for X: Finding the Value in (1/8)x + (2/3)x = 3

Q: Why can't I just add 1/8 and 2/3 directly?

You need a common denominator to add fractions! Just like you can't add 1 apple and 2 oranges to get 3 of something, you need the same "unit" (denominator) to combine fractions.

Q: How do I find the LCD of 8 and 3?

Since 8 and 3 share no common factors, their LCD is simply $ 8 \times 3 = 24 $. For other numbers, find the smallest number both denominators divide into evenly.

Q: How do I convert my answer to a mixed number?

Divide the numerator by the denominator: 72 ÷ 19 = 3 remainder 15, so $ \frac{72}{19} = 3\frac{15}{19} $.

Q: Do I always need to clear fractions first?

Not always, but it's usually much easier! You could work with fractions throughout, but clearing them first prevents calculation errors and makes combining like terms simpler.

Linear Equations with Fractional Coefficients

Solve for X:

$\frac{1}{8}x+\frac{2}{3}x=3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 We want to isolate the unknown X

00:08 We'll multiply by the common denominator to eliminate fractions

00:30 We'll reduce what we can

00:41 We'll solve each multiplication separately

00:55 We'll group like terms

01:04 We'll isolate the unknown X

01:20 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:

$\frac{1}{8}x+\frac{2}{3}x=3$

Step-by-step solution

To solve the equation $\frac{1}{8}x + \frac{2}{3}x = 3$ , we need to clear the fractions by finding the least common denominator.

Step 1: Identify the least common denominator of the fractions.
The denominators are 8 and 3. The least common denominator (LCD) is 24.

Step 2: Rewrite the equation with the LCD to get rid of the fractions:
Multiply each term by 24:
$24 \times \frac{1}{8} x + 24 \times \frac{2}{3} x = 24 \times 3$ .

Step 3: Simplify each term:
$\frac{24}{8}x = 3x$ ,
$\frac{24}{3}x = 16x$ ,
Thus, the equation becomes $3x + 16x = 72$ .

Step 4: Combine like terms:
$19x = 72$ .

Step 5: Solve for $x$ by dividing both sides by 19:
$x = \frac{72}{19}$ .

Convert the improper fraction to a mixed number:
Divide 72 by 19, which gives 3 with a remainder of 15. Thus, $x = 3\frac{15}{19}$ .

Therefore, the solution to the problem is $x = 3\frac{15}{19}$ .

Final Answer

$3\frac{15}{19}$

Key Points to Remember

Essential concepts to master this topic

LCD Method: Find common denominator to eliminate all fractions at once
Technique: Multiply entire equation by 24: $24 \times \frac{1}{8}x = 3x$
Check: Substitute $x = 3\frac{15}{19}$ back into original equation equals 3 ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without common denominator
Don't try to combine $\frac{1}{8}x + \frac{2}{3}x$ directly = wrong coefficients! You can't add fractions with different denominators. Always find the LCD first and convert both fractions before combining terms.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just add 1/8 and 2/3 directly?

You need a common denominator to add fractions! Just like you can't add 1 apple and 2 oranges to get 3 of something, you need the same "unit" (denominator) to combine fractions.

How do I find the LCD of 8 and 3?

Since 8 and 3 share no common factors, their LCD is simply $8 \times 3 = 24$ . For other numbers, find the smallest number both denominators divide into evenly.

What if I multiply by the wrong number?

Your equation will still be valid, just more complicated! If you multiply by 48 instead of 24, you'll get $6x + 32x = 144$ , which gives the same answer but with bigger numbers.

How do I convert my answer to a mixed number?

Divide the numerator by the denominator: 72 ÷ 19 = 3 remainder 15, so $\frac{72}{19} = 3\frac{15}{19}$ .

Do I always need to clear fractions first?

Not always, but it's usually much easier! You could work with fractions throughout, but clearing them first prevents calculation errors and makes combining like terms simpler.

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