Solving Equations Discussion
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 Post:
1. Equation 1: 5x + 3 = 18
Equation 2: 8x - 2 = 5x + 9
2. Open equation: 2x + 4 = 10
Response to #1:
Equation 1 is true because when we solve it, we get x = 3. Substituting the value of x in the equation, we have 5(3) + 3 = 18, which simplifies to 15 + 3 = 18, and this is true.
On the other hand, equation 2 is false because when we solve it, we get x = -11. Substituting the value of x in the equation, we have 8(-11) - 2 = 5(-11) + 9, which simplifies to -88 - 2 = -55 + 9, and this is false.
Response to #2:
To solve the open equation 2x + 4 = 10, we can start by isolating the variable x. Subtracting 4 from both sides of the equation, we have 2x = 6. And to find the value of x, we can divide both sides of the equation by 2, which gives us x = 3. So, the value of x that makes the equation true is x = 3.
Original Discussion Post:
1. Equation 1: 2x + 5 = 15
Equation 2: 3x - 7 = 10
2. Open equation: 4x + 2 = 3(2x + 1)
Solve for x.
Response to #1:
To determine which equation is true and which one is false, we need to solve each equation and check if the values of x satisfy the equations.
For Equation 1:
2x + 5 = 15
Subtracting 5 from both sides:
2x = 10
Dividing both sides by 2:
x = 5
For Equation 2:
3x - 7 = 10
Adding 7 to both sides:
3x = 17
Dividing both sides by 3:
x = 17/3
Comparing the values, we find that x = 5 satisfies Equation 1, while x = 17/3 satisfies Equation 2. Therefore, Equation 1 is true, and Equation 2 is false.
Response to #2:
To solve the open equation 4x + 2 = 3(2x + 1), we need to distribute the 3 to the terms inside the parentheses first.
4x + 2 = 3(2x + 1)
4x + 2 = 6x + 3
Next, we can rearrange the equation by subtracting 4x from both sides to isolate the variables on one side.
4x - 4x + 2 = 6x - 4x + 3
2 = 2x + 3
To isolate x, we can subtract 3 from both sides.
2 - 3 = 2x + 3 - 3
-1 = 2x
Finally, divide both sides by 2 to solve for x.
-1/2 = x
Therefore, the value of x that satisfies the equation 4x + 2 = 3(2x + 1) is x = -1/2.