compound inequalities
-10<-2+8x<22
break into two equations
So we get -10 < -2 +8x and -2+8x<22
now we have -8<8x and 8x<24
so we have -1<x and x<3
thus
-1<x<3
To solve the compound inequality -10 < -2 + 8x < 22, we will break it down into two separate inequalities and solve them individually.
First, we'll solve the inequality -10 < -2 + 8x:
-10 < -2 + 8x
Next, we'll solve the inequality -2 + 8x < 22:
-2 + 8x < 22
Now, let's solve each inequality one by one:
1. -10 < -2 + 8x:
Adding 2 to both sides gives us:
-10 + 2 < -2 + 2 + 8x
Simplifying further:
-8 < 8x
Finally, dividing both sides by 8, we have:
-8/8 < 8x/8
Simplifying:
-1 < x
So, the first inequality is -1 < x.
2. -2 + 8x < 22:
Adding 2 to both sides gives us:
-2 + 2 + 8x < 22 + 2
Simplifying further:
8x < 24
Finally, dividing both sides by 8, we have:
8x/8 < 24/8
Simplifying:
x < 3
So, the second inequality is x < 3.
Combining the two solutions, we get -1 < x < 3.