Hi guys! I just had a overdue assignment in math. I am a little lost in this topic, so I was hoping someone could help me out? Thanks!
Tell whether each equation is true, false, or open. Explain.
1. 6 - t = 12
2. 7 + (-5) = 12
3. 31 - 15 = 22 + (-3)2
If anyone knows how to figure out these equations, I would love to have them share. Thank you!
- Lupa
Okay, I was working some of them out. I believe that #1 is a true equation, but I am not for sure.
Oops, sorry meant false. Is it correct?
#1 is open
It can be true or false, depending on the value of t.
Now check the others to see whether they are always true or always false. That is, evaluate both sides.
Hi Lupa! I'd be happy to help you with these equations and explain how to determine if they are true, false, or open.
To evaluate the equations, we need to manipulate the expressions on both sides of the equation to see if they are equal or not. Let's go through each equation one by one:
1. 6 - t = 12
To solve this equation, we need to isolate the variable t on one side of the equation. Let's start by getting rid of the 6 on the left side. We can do this by subtracting 6 from both sides of the equation:
6 - t - 6 = 12 - 6
Simplifying, we have:
-t = 6
To isolate the variable t, we can multiply both sides of the equation by -1 to keep the equation balanced:
(-1)(-t) = (-1)(6)
t = -6
So, the solution to the equation is t = -6. This means it is a true statement.
2. 7 + (-5) = 12
In this equation, we need to simplify the expression on the left side of the equation:
7 + (-5) = 2
Now, we can compare the left side (2) with the right side (12). Since 2 is not equal to 12, this equation is false.
3. 31 - 15 = 22 + (-3)2
To solve this equation, we need to simplify both sides:
31 - 15 = 22 + (-3)2
16 = 22 + (-6)
Next, we simplify the expression on the right side:
16 = 22 - 6
16 = 16
In this case, the left side (16) is equal to the right side (16). Therefore, this equation is true.
In summary:
1. 6 - t = 12 is true, with the solution t = -6.
2. 7 + (-5) = 12 is false.
3. 31 - 15 = 22 + (-3)2 is true.
I hope this explanation helps you understand how to evaluate these equations. If you have any further questions, feel free to ask!