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.
1. Equation 1: 3x + 5 = 20
Equation 2: 2x - 7 = 10
2. Open Equation: 2(x + 4) = 8x - 6
1. Equation 1: 3x + 2 = 8
Equation 2: 4x - 5 = 7x - 6
2. Open Equation: 2x + 5 = 3(x + 2) - 7
Now, let's analyze these equations and determine which one is true and which one is false.
For Equation 1 (3x + 2 = 8), we can solve it step-by-step as follows:
Step 1: Subtract 2 from both sides:
3x = 6
Step 2: Divide both sides by 3:
x = 2
For Equation 2 (4x - 5 = 7x - 6), we can solve it step-by-step as follows:
Step 1: Subtract 4x from both sides:
-5 = 3x - 6
Step 2: Add 6 to both sides:
1 = 3x
Step 3: Divide both sides by 3:
1/3 = x
So, Equation 1 is true when x = 2, while Equation 2 is false when x = 1/3.
Moving on to the open equation (2x + 5 = 3(x + 2) - 7), let's solve it step-by-step:
Step 1: Distribute 3 to (x + 2):
2x + 5 = 3x + 6 - 7
Step 2: Combine like terms:
2x + 5 = 3x - 1
Step 3: Subtract 2x from both sides:
5 = x - 1
Step 4: Add 1 to both sides:
6 = x
Therefore, the value of x that makes the open equation true is x = 6.