-18<3x-7<-6
this question is asking for the solution. {x|x<x< -11/3, 1,3} is what i think it is
-18<3x-7<-6 , add 7
-11 < 3x < 1 , now divide by 3
-11/3 < x < 1/3
now write it as
{x│ -11/3 < x < 1/3 }
To solve the inequality -18 < 3x - 7 < -6, we will break it down into two separate inequalities and solve each one separately.
Let's start by solving the left side inequality, -18 < 3x - 7.
1. Add 7 to both sides of the inequality:
-18 + 7 < 3x - 7 + 7
-11 < 3x
2. Divide both sides of the inequality by 3:
(-11) / 3 < (3x) / 3
-11/3 < x
Now let's solve the right side inequality, 3x - 7 < -6.
1. Add 7 to both sides of the inequality:
3x - 7 + 7 < -6 + 7
3x < 1
2. Divide both sides of the inequality by 3:
(3x) / 3 < 1 / 3
x < 1/3
Therefore, the solution to the initial inequality -18 < 3x - 7 < -6 is -11/3 < x < 1/3.