I have some problems that I've answered and I need someone to check to see if I'm right. Im just posting the questons and my answer,if its wrong I'll post my work,so here it is bear with me please and thank you.
1)name which sets of numbers to which -28 belongs. my answer = integers,rationals,reals
2)the property illustrated by 7x(9+1)=(9+1)x7 is the. my answer = commutative property of multiplication
3)solve the equation 2/5y=3/14. my answer = 28/15
4)solve the equation 3(absolute value bars x-5)=12. my answer = null set
5)solve the equation (absolute bars y-8)+6=15. my answer = 17 I'll stop here for right now.
3. If y is in the denominator, you are right.
4. No, x=9 works, as does x=1
5. y-8=± 9 so y=8±9
Let's go through each question and analyze your answers:
1) Naming the sets to which -28 belongs:
Your answer is correct. -28 belongs to the set of integers (since it is a whole number), rationals (since it can be expressed as a fraction), and reals (since it is a real number).
2) Identifying the property illustrated by 7x(9+1)=(9+1)x7:
Again, your answer is correct. The property illustrated here is the commutative property of multiplication. This property states that the order of multiplication does not affect the result, so a x b = b x a.
3) Solving the equation 2/5y=3/14:
Your answer, 28/15, is incorrect. To solve this equation, we need to isolate the variable y. We can do this by multiplying both sides of the equation by the reciprocal of 2/5, which is 5/2. Multiplying both sides by 5/2 gives us:
(5/2) * (2/5)y = (5/2) * (3/14)
Canceling out the common factors, we obtain:
1y = 15/14
Simplifying gives:
y = 15/14
4) Solving the equation 3| x-5 | = 12:
Your answer, null set, is incorrect. To solve this equation, we need to eliminate the absolute value bars. We do this by considering two cases: positive and negative. For the positive case (x-5 > 0), we have:
3(x-5) = 12
Solving for x gives:
x = 9
For the negative case (x-5 < 0), we have:
3(-(x-5)) = 12
Simplifying gives:
3(5-x) = 12
15 - 3x = 12
Solving for x gives:
x = 1
Therefore, the solutions to the equation are x = 9 and x = 1.
5) Solving the equation | y-8 | + 6 = 15:
Your answer, 17, is incorrect. To solve this equation, we need to eliminate the absolute value bars. We do this by considering two cases: positive and negative. For the positive case (y-8 > 0), we have:
(y-8) + 6 = 15
Simplifying gives:
y - 2 = 15
Solving for y gives:
y = 17
For the negative case (y-8 < 0), we have:
-(y-8) + 6 = 15
Simplifying gives:
- y + 8 + 6 = 15
14 - y = 15
Solving for y gives:
y = -1
Therefore, the solutions to the equation are y = 17 and y = -1.
It is important to double-check your work to ensure accuracy in solving these problems.