Question

Which equation is modeled below?

4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles.

2 x + (negative 2) = negative 2 x + 6
4 x + (negative 2) = negative 2 x + 6
2 x + 4 = 6 x + 2
Negative 2 x + 4 = 6 x + (negative 2)

Answer 1

The correct equation modeled by the statement 4 x tiles and 2 negative 1 tiles equals 2 x tiles and 4 1 tiles is 4x - 2 = 2x + 4, following basic rules of algebra and properties of equality.

Step-by-step explanation:

We are asked to determine which equation is modeled by the following statement:

4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles.

To translate this into an equation, consider the following steps:

• Positive 'x' tiles represent positive x terms in the equation.
• Negative '1' tiles represent -1 in the equation.
• We then combine these 'tiles' into algebraic expressions according to their representations.

Following these steps, the equation becomes:

4x + (-2) = 2x + 4

Thus, the correct equation modeled by the given statement is:

4x - 2 = 2x + 4

This equation abides by the rules for adding and subtracting integers, as well as the properties of equality, which affirm that we can add or subtract the same number from both sides of an equation without changing the equation's balance.