Label each statement true or false if false correct the underlined portion.If -4<-2t+6<10,then this is the underlined 2>t+6>-5.
If this is underlined |y+8|+2=6,then this not underlined y+8=_+4.
Translate and solve.
the absolute value of three times a number,n,is greater than 15.
1. -4<-2t+6<10.
-10<-2t<4
Divide by -2 and reverse inequality sign:
5 > t > -2. True.
2. |y+8|+2 = 6.
|y+8| = 6-2 = 4
y+8 = +-4
Y = -8 +-4
Y = -4.
Y = -12.
3. |3n| > 15.
3n > 15
n > 5.
Which statement is true about the underlined digit in the number 1,466
Statement 1: False. The correct underlined form should be 2 > t + 6 > -5.
To determine if the underlined portion is correct, we need to work with each inequality separately.
The given compound inequality is -4 < -2t + 6 < 10.
First, let's isolate t in the middle inequality:
-4 < -2t + 6 < 10
Subtract 6 from all three parts of the inequality:
-4 - 6 < -2t < 10 - 6
-10 < -2t < 4
Divide all three parts by -2, but remember to flip the inequality signs whenever we multiply or divide by a negative number:
-10 / -2 > -2t / -2 > 4 / -2
5 > t > -2
So, the correct underlined form is 5 > t + 6 > -2, not 2 > t + 6 > -5.
Statement 2: True. Since the absolute value of a number can never be negative, the correct form is y + 8 = -4 + 6.
Let's solve it:
|y + 8| + 2 = 6
Subtract 2 from both sides:
|y + 8| = 4
Now we have two cases:
Case 1: y + 8 = 4
Subtract 8 from both sides:
y = 4 - 8
y = -4
Case 2: -(y + 8) = 4
Multiply both sides by -1 to remove the negative sign:
y + 8 = -4
Subtract 8 from both sides:
y = -4 - 8
y = -12
So the solution is y = -4 or y = -12.
Statement 3: Translate and solve.
"The absolute value of three times a number, n, is greater than 15."
Translate this into an inequality:
|3n| > 15
To solve this inequality, we need to consider two cases:
Case 1: 3n > 15
Divide both sides by 3:
n > 5
Case 2: -(3n) > 15
Divide both sides by -3, remembering to flip the inequality sign:
n < -5
So, the solution to the inequality is n < -5 or n > 5.