The problem involves solving for $x$ in the context of the area of a rectangle. Let me transcribe and analyze the problem for clarity:

Given problem: "Write an equation and solve for $x$ if the area of this rectangle is $133$ square units."

The rectangle's dimensions seem to involve $3x - 2$ for one side and $7$ for the other. To find the equation: $\text{Area of rectangle} = \text{length} \times \text{width}.$

From the problem, the equation is: $(3x - 2) \cdot 7 = 133.$

Let’s solve step-by-step:

Step 1: Expand the equation

$7(3x - 2) = 133.$ Distribute: $21x - 14 = 133.$

Step 2: Isolate $21x$

Add $14$ to both sides: $21x = 133 + 14,$ $21x = 147.$

Step 3: Solve for $x$

Divide both sides by $21$: $x = \frac{147}{21},$ $x = 7.$

Final Answer:

$x = 7.$

Would you like further details or explanations? Below are five related questions to expand on the topic:

Related Questions:

1. How do you solve for $x$ when dealing with other shapes like parallelograms or triangles?
2. What happens if the rectangle's area is given in terms of another variable (e.g., $y$) instead of a number?
3. How can you verify if the solution for $x$ satisfies the original area equation?
4. Can you explain how to rearrange equations involving multiple variables to isolate one variable?
5. What is the significance of units (e.g., square units) in these types of geometry problems?

Math Tip:

Always double-check your solution by substituting the value of $x$ back into the original equation to ensure it satisfies the problem's conditions.