Are the following expressions equivalent to $$ 42+28 x $$ ? $$ 6(7+4 x) $$ $$ 7(6 \downarrow 4 x) $$

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Let's analyze each expression to determine if it is equivalent to $$ 42 + 28x $$.

### 1. $$ 6(7 + 4x) $$

Using the distributive property:
$$
6(7 + 4x) = 6 \times 7 + 6 \times 4x = 42 + 24x
$$
**Comparison:**
$$
42 + 24x \quad \text{vs} \quad 42 + 28x
$$
These are **not** equivalent because $$ 24x \neq 28x $$.

### 2. $$ 7(6 \downarrow 4x) $$

The symbol $$ \downarrow $$ can have various meanings depending on the context, but it's not a standard arithmetic operator like addition, subtraction, multiplication, or division. Here are a few possible interpretations:

- **If $$ \downarrow $$ Represents Subtraction:**
  $$
  6 \downarrow 4x = 6 - 4x
  $$
  Then:
  $$
  7(6 - 4x) = 42 - 28x
  $$
  **Comparison:**
  $$
  42 - 28x \quad \text{vs} \quad 42 + 28x
  $$
  These are **not** equivalent because $$ -28x \neq +28x $$.

- **If $$ \downarrow $$ Represents Some Other Operation:**
  Without a clear definition of the $$ \downarrow $$ operator in this context, it's impossible to determine equivalence. However, under common mathematical interpretations, none would make $$ 7(6 \downarrow 4x) $$ equal to $$ 42 + 28x $$.

### **Conclusion**

Neither $$ 6(7 + 4x) $$ nor $$ 7(6 \downarrow 4x) $$ are equivalent to $$ 42 + 28x $$ based on standard mathematical interpretations.

**Summary:**
- $$ 6(7 + 4x) = 42 + 24x $$ ❌
- $$ 7(6 \downarrow 4x) $$ is not equivalent to $$ 42 + 28x $$ under standard interpretations ❌

**Final Answer:**
No; neither expression is equal to 42 + 28 x under standard mathematical interpretations.
Neither $$ 6(7 + 4x) $$ nor $$ 7(6 \downarrow 4x) $$ is equivalent to $$ 42 + 28x $$.

Are the following expressions equivalent to \( 42+28 x \) ? \( 6(7+4 x) \) \( 7(6 \downarrow 4 x) \)

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