Let's analyze the problem step by step based on the equations shown in the image.

Original Equation:

$x - 0.1x = 56.70$ This equation suggests that an unknown value $x$ is reduced by 10% (i.e., $0.1x$) to result in 56.70. The goal is to check if modifications in Equations D, E, and F lead to the same solution as the original.

Equation D:

$x - 0.1x = 56.70$

• What was done?
  No changes were made to this equation. It is exactly the same as the original.

• Interpretation:
  The price after applying a 10% discount (before tax) is $56.70$.

• Same solution?
  Yes, this equation is identical to the original, so it will have the same solution.

Equation E:

$x - 0.1x = 59.40$

• What was done?
  The right-hand side of the equation has been changed from 56.70 to 59.40, indicating an increase of 2.70.

• Interpretation:
  This could suggest that $59.40$ is the total price after a discount, but possibly before tax, or there might be a fee added.

• Same solution?
  No, this is a different equation, as the result of the discount is different. This would yield a different value for $x$.

Equation F:

$2(x - 0.1x + 2.70) = 56.70$

• What was done?
  The equation is multiplied by 2, and 2.70 is added inside the parentheses, potentially accounting for an additional fixed cost or fee applied after the discount.

• Interpretation:
  This equation could represent the price for two pairs of jeans after applying the 10% discount, with each pair being priced at $x - 0.1x + 2.70$.

• Same solution?
  This equation will not have the same solution as the original. The introduction of the factor 2 and the additional 2.70 significantly alters the equation.

Question 4:

• Which of the six equations are equivalent to the original equation?

The only equation that is equivalent to the original is Equation D, as it is identical to the original equation $x - 0.1x = 56.70$.

Let me know if you want more details or have questions.

Here are 5 related questions for further learning:

1. What is the solution for $x$ in the original equation?
2. How does changing the constant on the right side of the equation affect the solution for $x$?
3. How can you interpret the result of $x - 0.1x$ in real-world terms like discounts?
4. What would happen if you applied both a 10% discount and an additional fixed fee to the original price $x$?
5. Can you solve Equation F to find the value of $x$?

Tip:

When solving equations with percentages, always ensure that you are clear whether the percentage is applied before or after other operations, such as adding taxes or fees.