*"<_" is less than equal to*
5) -15<x-8<-4
6)12<_4n<28
7)-2<_3b+7<_13
for "less than or equal to" use the left carat key "<" along with the "alt option" key to get "≤".
just solve both sides at once.
-15<x-8<-4
add 8 everywhere:
-15+8 < x-8+8 < -4+8
-7 < x < 4
what do you get for the others?
To solve inequalities such as these, we'll follow a similar process. Let's break it down step-by-step for each inequality:
5) -15 < x-8 < -4
First, let's isolate the variable by adding 8 to all sides of the inequality:
-15 + 8 < x-8 + 8 < -4 + 8
Simplifying further, we get:
-7 < x < 4
So the solution to the inequality is x lies between -7 and 4, not including these endpoints.
6) 12 <= 4n < 28
To solve this inequality, we'll divide both sides of the inequality by 4:
12/4 <= 4n/4 < 28/4
This simplifies to:
3 <= n < 7
Therefore, n lies between 3 and 7, including 3 but not including 7.
7) -2 <= 3b + 7 <= 13
First, let's isolate the variable by subtracting 7 from all sides of the inequality:
-2 - 7 <= 3b + 7 - 7 <= 13 - 7
This simplifies to:
-9 <= 3b <= 6
Next, let's divide all sides of the inequality by 3:
-9/3 <= 3b/3 <= 6/3
This further simplifies to:
-3 <= b <= 2
So the solution to the inequality is b lying between -3 and 2, including both endpoints.