Hi, I need some help on my homework.
Can you help me?
True or False, if False correct the underlined portion.
1) If 3<x, then 3+y<x+y
2)If |w-7|<-3, then w-7>-3 or w-7<3
3) If -4<-2t+6<10, then 2>t+6>-5
4) If |y+8|+2=6, then y+8=+-4*
* the "+" is on top of "-", I didn't know how to type it in.
I would really appreciate the help.
1 is true
2 makes no sense/ an absolute value can not be negative.
3 but t = 0 ok for first but not for second
4 you mean
4) If |y+8|+2=6, then y+8=+/- 4
y + 8 + 2 = 6
then y = -4
-(y+8) + 2 = 6
-y - 8 + 2 = 6
- y - 6 = 6
-y = 12 NO or false
+/-4 means plus or - 4
Damon,
thank you so much!!
This helped a lot!
Of course, I'll be happy to help you with your homework. Let's go through each statement and determine if it's true or false.
1) If 3 < x, then 3 + y < x + y.
This statement is true. When you add the same number to both sides of an inequality, the inequality remains unchanged.
2) If |w - 7| < -3, then w - 7 > -3 or w - 7 < 3.
This statement is false. The absolute value of any number is always non-negative, so it can never be less than a negative number. Thus, the correct statement would be:
If |w - 7| < -3, then there are no solutions.
3) If -4 < -2t + 6 < 10, then 2 > t + 6 > -5.
This statement is true. To solve this compound inequality, we can subtract 6 from all sides, giving:
-10 < -2t < 4
Then, divide all terms by -2. However, when dividing by a negative number, the inequality sign flips, resulting in:
5 > t > -2
This is equivalent to 2 > t + 6 > -5.
4) If |y + 8| + 2 = 6, then y + 8 = ±4.
This statement is true. To solve this equation, we first subtract 2 from both sides, giving:
|y + 8| = 4
The absolute value of a number can be positive or negative, depending on whether the argument inside the absolute value is positive or negative. Therefore, we have two cases to consider:
Case 1: y + 8 = 4
In this case, we subtract 8 from both sides, resulting in:
y = -4
Case 2: -(y + 8) = 4
Here, we distribute the negative sign and solve for y:
-y - 8 = 4
By adding 8 to both sides and multiplying by -1, we find:
y = -12
So, the underlined portion is correct as "y + 8 = ±4."
I hope this helps! Let me know if you have any further questions.