If (x + 3), (x - 9) & (x - 3) are in proportion then x = ?

If \((x + 3)\), \((x - 9)\), and \((x - 3)\) are in proportion, we can use the concept of ratios.

Given that these expressions are in proportion, we have:

\[
\frac{x + 3}{x - 9} = \frac{x - 9}{x - 3}
\]

To solve for \(x\), we'll cross-multiply:

\[
(x + 3) \times (x - 3) = (x - 9) \times (x - 9)
\]

Let's expand both sides:

Left-hand side:

\[
(x + 3)(x - 3) = x^2 - 9
\]

Right-hand side:

\[
(x - 9)(x - 9) = x^2 - 18x + 81
\]

So the equation becomes:

\[
x^2 - 9 = x^2 - 18x + 81
\]

Subtract \(x^2\) from both sides:

\[
-9 = -18x + 81
\]

Subtract 81 from both sides:

\[
-9 - 81 = -18x
\]

\[
-90 = -18x
\]

Divide both sides by -18:

\[
x = \frac{90}{18} = 5
\]

So, the value of \(x\) is \(5\).

Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you solve a proportion involving quadratic expressions?
2. What are the steps to solve equations with cross-multiplication?
3. How can you identify whether terms are in proportion?
4. What happens when the expressions are in inverse proportion?
5. How does simplifying expressions affect solving proportions?

**Tip:** When expanding binomials like \((a + b)(a - b)\), use the difference of squares formula: \(a^2 - b^2\).

Learn how to solve proportions involving quadratic expressions such as (x + 3), (x - 9), and (x - 3) using cross-multiplication. This problem illustrates key algebraic concepts and formulas for ratios. Suitable for high school students studying algebra.

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