https://file.aiquickdraw.com/mathbot/file/1728233639945r8at3ckv.jpg

The image shows four mathematical word problems in Arabic, and their corresponding equations are highlighted. The word problems ask to translate the statements into equations. However, two of the answers have been marked incorrect (with red X's).

Let me walk through the problems and their corresponding equations:

1. **Three times a number minus eight equals 21:**
   \[
   3x - 8 = 21
   \]
   This equation is correct.

2. **Three more than one-third of a number equals 7:**
   This should be written as:
   \[
   \frac{1}{3}x + 3 = 7
   \]
   The incorrect equation marked is \( \frac{x}{3} - 3 = 7 \), which was marked wrong because the subtraction should be addition.

3. **Three less than six times a number equals 18:**
   This should be:
   \[
   6x - 3 = 18
   \]
   This is correct in the image.

4. **The difference between twice a number and 2 equals 3:**
   This should be:
   \[
   2x - 2 = 3
   \]
   The incorrect equation marked is \( \frac{2}{x} - x = 3 \), which is wrong because the word problem describes a linear equation, not a rational one.

Would you like more details or explanations? Here are five related questions you could explore:

1. How do you solve the equation \( \frac{1}{3}x + 3 = 7 \)?
2. Can you describe how to rearrange and solve \( 2x - 2 = 3 \)?
3. What is the method to solve \( 3x - 8 = 21 \) step by step?
4. How do you verify if a given equation represents a word problem correctly?
5. What are common mistakes made when translating word problems into equations?

**Tip**: Always check if the operations described in word problems match the operations in the equation (addition vs. subtraction, multiplication vs. division).

Translate the following sentences into equations:
1. Three times a certain number minus eight equals 21.
2. Three more than one-third of a certain number equals 7.
3. Three less than six times a certain number equals 18.
4. The difference between twice a certain number and 2 equals 3.

Learn how to translate real-world word problems into linear equations, including examples such as 'Three times a number minus eight equals 21' and 'Three more than one-third of a number equals 7'. Suitable for students in Grades 6-8.

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