Question

Solving Equations Discussion

Before engaging in the discussion, view the Discussion Guidelines and Discussion Rubric to ensure that you understand the expectations for this activity. Once you have posted your response, you are also required to respond to at least two other students' posts. You may want to check back later to respond to your classmates.

1. Make up two equations, one that is true and one that is false. Do not state which equation is true and which is false. Your classmates will have to determine which is which.

2. Create an example of an open equation that uses the variable x and would require two or more steps to solve. Your classmates will have to determine which value of x makes the equation true.

For your original discussion post, you only need to respond to #1 and #2.

3. View posts from your classmates and choose one to respond to. For #1 you will need to determine which equation is true and which equation is false and explain how you know. For #2 you will need to solve the equation that your classmate created, showing all of your steps and explaining your work.

4. View responses and comment on the work of another classmate. You may correct any errors that you find, show another way to solve the problem, or provide constructive feedback on the work.

Answer 1

Explanation:

Equations:

2x + 3 = 7x - 5

4x + 6 = 8x + 1

Open equation: 3x - 2 = 7x + 5

For #1, to determine which equation is true and which is false, we need to solve each equation for x and see which equation satisfies the solution.

Solving 2x + 3 = 7x - 5 for x, we get x = 2. Hence, 2x + 3 = 2(2) + 3 = 7 and 7x - 5 = 7(2) - 5 = 9. Thus, the equation 2x + 3 = 7x - 5 is false.

Solving 4x + 6 = 8x + 1 for x, we get x = 5/2. Hence, 4x + 6 = 4(5/2) + 6 = 16 and 8x + 1 = 8(5/2) + 1 = 21. Thus, the equation 4x + 6 = 8x + 1 is false.

For #2, we have the open equation 3x - 2 = 7x + 5, which requires two or more steps to solve. First, we can simplify the equation by moving the variable terms to one side and the constant terms to the other side.

Adding 2 to both sides, we get 3x = 7x + 7.

Subtracting 7x from both sides, we get -4x = 7.

Dividing both sides by -4, we get x = -7/4.

Thus, the value of x that makes the equation true is x = -7/4.