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.
Original Discussion Post:
1. Equation 1: 3x + 2 = 11
Equation 2: 4x - 5 = 2x + 10
2. Open equation: 2x + 5 = 3(x - 1)
Response:
For #1, Equation 1: 3x + 2 = 11 can be solved by isolating x and determining its value. Subtracting 2 from both sides of the equation, we have 3x = 9. Dividing both sides by 3, we find x = 3. Therefore, Equation 1 is true.
Equation 2: 4x - 5 = 2x + 10 can be solved in a similar way. First, let's subtract 2x from both sides of the equation: 2x - 5 = 10. Adding 5 to both sides, we obtain 2x = 15. Dividing both sides by 2, we find x = 7.5. Therefore, Equation 2 is false.
For #2, the open equation 2x + 5 = 3(x - 1) requires multiple steps to solve. Let's start by distributing the 3 to the terms inside the parentheses: 2x + 5 = 3x - 3. Next, let's subtract 2x from both sides of the equation: 5 = x - 3. Adding 3 to both sides, we get 8 = x. Therefore, the value of x that makes the equation true is 8.
Now, I will proceed to respond to a classmate's post.
1. Here are my two equations:
Equation 1: 3x + 5 = 20
Equation 2: 2x - 8 = 12
2. Open equation:
Equation: 4x + 3 = 2(x + 2)
Now I will respond to a classmate.
Response to classmate's Equation 1: 3x + 2 = 11
To determine whether this equation is true or false, I will substitute a value for x and see if the equation holds true. Let's say I choose x = 2.
Substituting x = 2 into the equation:
3(2) + 2 = 11
6 + 2 = 11
8 = 11
Since 8 is not equal to 11, this equation is false.
Response to classmate's Equation 2: 5x - 4 = 21
To determine whether this equation is true or false, I will again substitute a value for x and check if the equation holds true. Let's say I choose x = 5.
Substituting x = 5 into the equation:
5(5) - 4 = 21
25 - 4 = 21
21 = 21
Since 21 is equal to 21, this equation is true.
Response to classmate's open equation: 2x - 3 = 5(x + 1)
To solve this equation, we will first distribute the 5 on the right side:
2x - 3 = 5x + 5
Next, we will isolate the variable x on one side by subtracting 5x from both sides of the equation:
2x - 5x - 3 = 5x - 5x + 5
-3x - 3 = 5
To further isolate x, we will add 3 to both sides:
-3x - 3 + 3 = 5 + 3
-3x = 8
Finally, we divide both sides by -3 to solve for x:
(-3x)/-3 = 8/-3
x = -8/3
So the solution to the equation is x = -8/3.
For the first part of the discussion, let's start by making up two equations: one that is true and one that is false. Here are the equations:
Equation 1: 2 + 3 = 7
Equation 2: 5 - 2 = 3
Now, it's important not to state which equation is true and which is false. The goal is for your classmates to determine which is which.
For the second part of the discussion, let's create an example of an open equation that uses the variable x and requires two or more steps to solve. Here is an example:
Equation 3: 4x - 7 = 17
This equation involves multiplying the variable x by 4, subtracting 7, and setting it equal to 17. Your classmates will need to determine which value of x makes the equation true.
For your original discussion post, you only need to respond to #1 and #2. Make sure to provide explanations for your choices and any steps you took to solve the equations or find the value of x.