Solve for X: 1/8x - 2/3x + 1/5x = 1 Linear Equation

Q: How do I find the LCD of 8, 3, and 5?

Find the least common multiple of all denominators. Since 8 = 2³, 3 = 3, and 5 = 5 have no common factors, multiply them: $ 8 \times 3 \times 5 = 120 $.

Q: How do I verify this complicated answer?

Substitute $ x = -\frac{120}{41} $ back into $ \frac{1}{8}x - \frac{2}{3}x + \frac{1}{5}x = 1 $. If the left side equals 1, your answer is correct!

Linear Equations with Multiple Fractional Terms

Solve for X:

$\frac{1}{8}x-\frac{2}{3}x+\frac{1}{5}x=1$

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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

00:15 We'll divide 120 by each appropriate fraction

00:36 We'll solve each multiplication separately

00:50 We'll group the factors

01:01 We'll isolate the unknown X

01:15 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:

$\frac{1}{8}x-\frac{2}{3}x+\frac{1}{5}x=1$

Step-by-step solution

The common denominator of 8, 3, and 5 is 120.

Now we multiply each numerator by the corresponding number to reach 120 and thus cancel the fractions and obtain the following equation:

$(1\times x\times15)-(2\times x\times40)+(1\times x\times24)=1\times120$

We multiply the exercises in parentheses accordingly:

$15x-80x+24x=120$

We will solve the left side (from left to right) and will obtain:

$(15x-80x)+24x=120$

$-65x+24x=120$

$-41x=120$

We reduce both sides by $-41$

$\frac{-41x}{-41}=\frac{120}{-41}$

We find that x is equal $x=-\frac{120}{41}$

Final Answer

$-\frac{120}{41}$

Key Points to Remember

Essential concepts to master this topic

LCD Method: Find common denominator to clear all fractions at once
Technique: For denominators 8, 3, 5: LCD = 120, multiply all terms
Check: Substitute $x = -\frac{120}{41}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without finding LCD first
Don't try to combine $\frac{1}{8}x - \frac{2}{3}x + \frac{1}{5}x$ directly = messy calculations and errors! This makes the problem much harder and leads to wrong answers. Always find the LCD (120) first and multiply every term by it to clear all fractions.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

How do I find the LCD of 8, 3, and 5?

Find the least common multiple of all denominators. Since 8 = 2³, 3 = 3, and 5 = 5 have no common factors, multiply them: $8 \times 3 \times 5 = 120$ .

Why do I multiply each term by a different number?

You multiply each fraction by whatever makes its denominator equal to 120. For $\frac{1}{8}x$ , multiply by 15 because $8 \times 15 = 120$ . This clears the fraction completely!

What if my final answer is negative?

Negative answers are completely normal in algebra! The problem gives us $x = -\frac{120}{41}$ , which is correct. Always check by substituting back into the original equation.

Can I simplify the fraction -120/41?

Check if 120 and 41 share any common factors. Since 41 is prime and doesn't divide 120, the fraction is already in simplest form.

How do I verify this complicated answer?

Substitute $x = -\frac{120}{41}$ back into $\frac{1}{8}x - \frac{2}{3}x + \frac{1}{5}x = 1$ . If the left side equals 1, your answer is correct!

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