solve and write in interval notation
|6x+2|<18
-18<6x+2<18
10/3<x<8/3
(-10/3,8/3)
You probably just had a typo by leaving out the - in front of 10/3 in your second last line
it should say
-10/3<x<8/3
Why are you writing the endpoints as an ordered pair (-10/3,8/3)?
Are "they" showing you to do that?
math -9h-6+12h+40=22
To solve the inequality |6x+2|<18 in interval notation, we need to break it down into two separate inequalities and then find the intersection of their solution sets.
First, we need to eliminate the absolute value by considering the two cases:
Case 1: (6x + 2) is positive (since |6x+2| is positive):
In this case, the inequality becomes:
6x + 2 < 18
Let's solve it for x:
6x < 18 - 2
6x < 16
x < 16/6
x < 8/3
So for this case, the solution is x < 8/3.
Case 2: (6x + 2) is negative (since |6x+2| is positive):
In this case, the inequality becomes:
-(6x + 2) < 18
Let's solve it for x, remembering to reverse the inequality when multiplying by -1:
6x + 2 > -18
6x > -18 - 2
6x > -20
x > -20/6
x > -10/3
So for this case, the solution is x > -10/3.
Now, we need to find the intersection of the solutions from Case 1 and Case 2. This means we need to find the values of x that satisfy both inequalities simultaneously.
The intersection of the two solution sets is given by the condition:
x < 8/3 and x > -10/3
In interval notation, we write this as:
(-10/3, 8/3)