Question

Garcia is modeling the equation 5 x + (negative 1) = negative 2 x + 6 by using the following tiles:

5 positive x-tiles and 1 positive unit tile to represent 5x + (– 1)
2 negative x-tiles and 6 positive unit tiles to represent –2x + 6

Which statement explains Garcia’s error?
Garcia should have used 5 positive x-tiles and 1 negative unit tile to represent 5x + (–1).
Garcia should have used 2 positive x-tiles and 6 positive unit tiles to represent –2x + 6.
Garcia should have used 1 negative x-tile and 5 positive unit tiles to represent 5x + (–1), and he should have used 6 positive x-tiles and 2 negative unit tiles to represent –2x + 6.
Garcia should have used 5 negative x-tiles and 1 positive unit tile to represent 5x + (–1), and he should have used 2 positive x-tiles and 6 negative unit tiles to represent –2x + 6.
Answer
Sherry uses the steps below to solve the equation x + (negative 8) = 3 x + 6.

Step 1 Add 1 negative x-tile to both sides and create zero pairs
Step 2 Add 8 positive unit tiles to both sides and create zero pairs.
Step 3 Divide the 14 unit tiles evenly among the 2 x-tiles.
Step 4 The solution is x = 7

What is Sherry’s error?
In step 1, she should have added 3 negative x-tiles to both sides.
In step 2, she should have added 6 negative unit tiles to both sides.
In step 3, she did not divide the tiles evenly.
In step 4, she should have found the solution x = negative 1.
Answer
Dante wrote several equations and determined that only one of the equations has infinitely many solutions. Which of these equations has infinitely many solutions?
6 (x + 3) + x = 7 x + 2 + 1
6 (x + 3) + x = 7 x + 5
6 (x + 3) + x = 6 x + 3 + 15
6 (x + 3) + x = 7 x + 9 + 9
Answered by Bot
Garcia should have used 1 negative x-tile and 5 positive unit tiles to represent 5x + (–1), and he should have used 6 positive x-tiles and 2 negative unit tiles to represent –2x + 6.
Answered by Bot
Sherry's error is in step 3. She should have divided the 14 unit tiles evenly among the 3 x-tiles, not 2 x-tiles. Therefore, the solution should be x = 4, not x = 7.
Answered by Bot
The equation that has infinitely many solutions is 6(x + 3) + x = 6x + 3 + 15.

When we simplify this equation, we get:

6x + 18 + x = 6x + 18

Combining like terms, we get:

7x + 18 = 6x + 18

Subtracting 6x and 18 from both sides, we get:

x = 0

So, the equation is true for any value of x. Therefore, it has infinitely many solutions.