https://r2.erweima.ai/mathbot/image/172666937453602cmox18.jpg

We are given the following proportion to solve:

\[
\frac{-2}{4x + 1} = \frac{7}{8}
\]

### Steps to solve:

1. **Cross-multiply**:
   Multiply both sides by the denominators to eliminate the fractions:
   \[
   -2 \times 8 = (4x + 1) \times 7
   \]
   This simplifies to:
   \[
   -16 = 7(4x + 1)
   \]

2. **Distribute** the 7 on the right-hand side:
   \[
   -16 = 28x + 7
   \]

3. **Isolate the term** with \( x \):
   Subtract 7 from both sides:
   \[
   -16 - 7 = 28x
   \]
   \[
   -23 = 28x
   \]

4. **Solve for \( x \)**:
   Divide both sides by 28:
   \[
   x = \frac{-23}{28}
   \]

Thus, the solution is:

\[
x = \frac{-23}{28}
\]

Would you like more details, or do you have any questions?

---

Here are five related questions to expand on this concept:

1. How can you check if the solution \( x = \frac{-23}{28} \) is correct?
2. What are the steps to solve a proportion when both fractions involve expressions with \( x \)?
3. Can you solve for \( x \) in the proportion \( \frac{5x + 2}{6} = \frac{3}{4} \)?
4. What happens if the proportion involves quadratic terms, such as \( \frac{x^2 - 1}{2} = \frac{5}{6} \)?
5. How do proportions change when the denominator of one side is zero?

**Tip:** Always double-check your cross-multiplication when solving proportions to avoid simple mistakes.

Solve the following proportion: (-2) / (4x + 1) = 7 / 8

Learn how to solve the proportion (-2) / (4x + 1) = 7 / 8 with a detailed step-by-step explanation. This algebraic problem focuses on using cross-multiplication to find the value of x. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation