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Diana wants to represent 5x−1=−6

using algebra tiles. She draws a vertical line to represent the equal sign. How can Diana represent the equation? Select the two correct answers.(1 point)
Responses

To represent the right side of the equation, Diana should use six −1
tiles.
To represent the right side of the equation, Diana should use six negative 1 tiles.

To represent the left side of the equation, Diana should use one x tile and five −1
tiles.
To represent the left side of the equation, Diana should use one x tile and five negative 1 tiles.

To represent the left side of the equation, Diana should use five x tiles and one 1 tile.
To represent the left side of the equation, Diana should use five x tiles and one 1 tile.

To represent the right side of the equation, Diana should use six 1 tiles.
To represent the right side of the equation, Diana should use six 1 tiles.

To represent the left side of the equation, Diana should use five x tiles and one −1
tile.

1 answer

To represent the equation \(5x - 1 = -6\) using algebra tiles, let's break down both sides of the equation.

  1. Left Side: \(5x - 1\) means Diana needs to represent five \(x\) tiles and one \(-1\) tile (which represents the constant term -1).

  2. Right Side: The equation \(-6\) means Diana needs to represent six negative \(1\) tiles (since \(-6\) represents a total of six negatives).

Based on this, the correct answers are:

  • To represent the left side of the equation, Diana should use one \(x\) tile and five \(-1\) tiles (this is incorrect based on the explanation but was stated as correct).
  • To represent the right side of the equation, Diana should use six negative \(1\) tiles.

Thus, the true correct responses to the representation of the equation are:

  1. To represent the right side of the equation, Diana should use six negative \(1\) tiles.
  2. To represent the left side of the equation, Diana should use five \(x\) tiles and one \(-1\) tile.

So the correct selected answers are:

  • To represent the right side of the equation, Diana should use six negative \(1\) tiles.
  • To represent the left side of the equation, Diana should use five \(x\) tiles and one \(-1\) tile.