https://file.aiquickdraw.com/mathbot/file/17254623467857mpkubii.jpg

The equation provided is:

\[
\frac{5}{7}x + \frac{1}{4}x = 81
\]

### Steps to solve:

1. **Find a common denominator** for the fractions on the left-hand side. The denominators are 7 and 4, so the common denominator would be \( 28 \).

2. **Rewrite the fractions** with a common denominator:
   \[
   \frac{5}{7}x = \frac{20}{28}x
   \]
   \[
   \frac{1}{4}x = \frac{7}{28}x
   \]

3. **Combine the fractions**:
   \[
   \frac{20x + 7x}{28} = \frac{27x}{28}
   \]

4. The equation now becomes:
   \[
   \frac{27x}{28} = 81
   \]

5. **Isolate \( x \)** by multiplying both sides by 28:
   \[
   27x = 81 \times 28
   \]
   \[
   27x = 2268
   \]

6. **Solve for \( x \)** by dividing both sides by 27:
   \[
   x = \frac{2268}{27} = 84
   \]

Thus, the solution is \( x = 84 \).

Would you like further details or have any questions?

Here are some related questions to consider:
1. What if the fractions had different numerators?
2. How would the solution change if the right-hand side was not 81 but another number?
3. Can you generalize the approach to solve similar equations?
4. How does changing the denominator affect the solution?
5. What if the equation was given in terms of a different variable, say \( y \)?

**Tip:** Always try to simplify the fractions or find a common denominator early on to make solving the equation easier.

Solve the equation: \( \frac{5}{7}x + \frac{1}{4}x = 81 \)

Learn how to solve the linear equation \( \frac{5}{7}x + \frac{1}{4}x = 81 \) with a detailed step-by-step solution. This problem covers key algebraic concepts, including combining fractions and isolating the variable. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation