(b) Los op vir $$ x $$ : (1) $$ \quad 2 a x+b=c x $$ (3) $$ a x^{2}-9 b^{2}=0 $$ (5) $$ \quad x^{2}+3 b x+2 b^{2}=0 $$ (7) $$ \quad x^{2}-2 b x+a x-2 a b=0 $$

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**(1) Solve $$2ax + b = cx$$:**  
Rearrange the equation to collect the terms with $$ x $$ on one side:  
$$
2ax + b = cx \implies 2ax - cx = -b.
$$  
Factor $$ x $$ from the left side:  
$$
x(2a - c) = -b.
$$  
Assuming $$2a - c \neq 0$$, solve for $$ x $$:  
$$
x = \frac{-b}{2a - c}.
$$

---

**(3) Solve $$ ax^2 - 9b^2 = 0 $$:**  
First, isolate the $$ x^2 $$ term by adding $$ 9b^2 $$ to both sides:  
$$
ax^2 = 9b^2.
$$  
Divide both sides by $$ a $$ (assuming $$ a \neq 0 $$):  
$$
x^2 = \frac{9b^2}{a}.
$$  
Take the square root of both sides, remembering to include both positive and negative roots:  
$$
x = \pm \sqrt{\frac{9b^2}{a}} = \pm \frac{3|b|}{\sqrt{a}}.
$$  
In many contexts (assuming $$ b $$ represents any real number), this result may also be written as:  
$$
x = \pm \frac{3b}{\sqrt{a}},
$$  
with the understanding that the sign of $$ b $$ is absorbed by the $$ \pm $$ symbol.

---

**(5) Solve $$ x^2 + 3bx + 2b^2 = 0 $$:**  
This quadratic can be factored. Look for two numbers that multiply to $$ 2b^2 $$ and sum to $$ 3b $$. These numbers are $$ b $$ and $$ 2b $$:  
$$
x^2 + 3bx + 2b^2 = (x + b)(x + 2b) = 0.
$$  
Set each factor equal to zero:  
$$
\begin{aligned}
x + b &= 0 \quad \implies \quad x = -b,\[1mm]
x + 2b &= 0 \quad \implies \quad x = -2b.
\end{aligned}
$$

---

**(7) Solve $$ x^2 - 2bx + ax - 2ab = 0 $$:**  
First, group the terms to factor by grouping:  
$$
x^2 - 2bx + ax - 2ab = \bigl(x^2 + ax\bigr) - \bigl(2bx + 2ab\bigr).
$$  
Factor $$ x $$ from the first group and $$ 2b $$ from the second group:  
$$
= x(x + a) - 2b(x + a).
$$  
Factor out the common binomial $$ (x + a) $$:  
$$
(x + a)(x - 2b) = 0.
$$  
Set each factor equal to zero:  
$$
\begin{aligned}
x + a &= 0 \quad \implies \quad x = -a,\[1mm]
x - 2b &= 0 \quad \implies \quad x = 2b.
\end{aligned}
$$

---

**Summary of Solutions:**

1. For $$ 2ax + b = cx $$:  
$$
x = \frac{-b}{2a - c}.
$$

2. For $$ ax^2 - 9b^2 = 0 $$:  
$$
x = \pm \frac{3b}{\sqrt{a}} \quad \text{(with appropriate interpretation of the square root)}.
$$

3. For $$ x^2 + 3bx + 2b^2 = 0 $$:  
$$
x = -b \quad \text{or} \quad x = -2b.
$$

4. For $$ x^2 - 2bx + ax - 2ab = 0 $$:  
$$
x = -a \quad \text{or} \quad x = 2b.
$$
Solutions for the equations are: 1. $$ x = \frac{-b}{2a - c} $$ 2. $$ x = \pm \frac{3b}{\sqrt{a}} $$ 3. $$ x = -b $$ or $$ x = -2b $$ 4. $$ x = -a $$ or $$ x = 2b $$

(b) Los op vir \( x \) : (1) \( \quad 2 a x+b=c x \) (3) \( a x^{2}-9 b^{2}=0 \) (5) \( \quad x^{2}+3 b x+2 b^{2}=0 \) (7) \( \quad x^{2}-2 b x+a x-2 a b=0 \)

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