To solve the equation:

\[
\frac{p+10}{p-7} = \frac{8}{9}
\]

we can use cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other fraction.

\[
9(p+10) = 8(p-7)
\]

Now, expand both sides:

\[
9p + 90 = 8p - 56
\]

Next, move all terms involving \( p \) to one side and constant terms to the other side. Subtract \( 8p \) from both sides:

\[
9p - 8p + 90 = -56
\]

Simplify:

\[
p + 90 = -56
\]

Now subtract 90 from both sides:

\[
p = -56 - 90
\]

\[
p = -146
\]

Thus, the solution is:

\[
p = -146
\]

Would you like more details or have any questions?

---

Here are 5 related questions to expand your understanding:

1. What is the general process for solving rational equations?
2. How can you verify the solution to this equation?
3. What happens if a rational equation has no solution?
4. Can you solve \(\frac{p+12}{p-5} = \frac{7}{10}\)?
5. How does cross-multiplication work with inequalities?

**Tip:** Always check your solution by substituting it back into the original equation to avoid errors.

Discover how to solve the rational equation (p+10)/(p-7) = 8/9 using cross-multiplication. This step-by-step solution explains the key algebraic concepts and provides a thorough breakdown. Ideal 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