please check these answers and change if needed. thank you
Label each statement true or false, if false change underlined portion.
C. if -4 < -2t + 6 < 10 then this is underlined 2 > t + 6 > -5 I marked false, i think it should be -2 < t < 5.
D. If |y + 8| + 2 + 6, this underlined
this is not underlined: y + 8 = +4 -4
i marked it true
C.
-4 < -2t+6 < 10
-10 < -2t < 4
5 > t > -2
-2 < t < 5
D.
is that |y+8| + 2 = 6 ?
if so, then
|y+8| = 4
y+8 = 4 or y+8 = - 4
y = -4 or y = -12
reiny thank you very much for your help, i mistyped the = so you have it right. i really appreciate your help. ann
C. -4 < -2t + 6 < 10
The goal is to isolate t in the inequality. Let's solve it step by step:
-4 < -2t + 6 < 10
First, subtract 6 from all three parts of the inequality:
-4 - 6 < -2t + 6 - 6 < 10 - 6
Simplifying:
-10 < -2t < 4
Next, divide all three parts of the inequality by -2 (remember to change the direction of the inequality because we are dividing by a negative number):
-10 / -2 > -2t / -2 > 4 / -2
Simplifying:
5 > t > -2
So, the correct statement is 5 > t > -2. You correctly marked it as false and suggested the correct answer, which is -2 < t < 5.
D. |y + 8| + 2 = 6
The goal is to solve for y in the equation. Let's solve it step by step:
|y + 8| + 2 = 6
First, subtract 2 from both sides of the equation:
|y + 8| = 6 - 2
Simplifying:
|y + 8| = 4
To remove the absolute value brackets, we can split the equation into two cases: one where y + 8 is positive, and one where it is negative.
Case 1: y + 8 > 0
In this case, the equation becomes:
y + 8 = 4
Solving for y:
y = 4 - 8
Simplifying:
y = -4
So, in case 1, y = -4.
Case 2: y + 8 < 0
In this case, the equation becomes:
-(y + 8) = 4
Solving for y:
-y - 8 = 4
Adding 8 to both sides:
-y = 4 + 8
Simplifying:
-y = 12
Multiplying both sides by -1 (remember to change the direction of the inequality because we are multiplying by a negative number):
y = -12
So, in case 2, y = -12.
Therefore, the correct statement should be:
y = -4 or y = -12, which means you marked it correctly as true.