8+b<-3
h/4>16
-7z<21
Good morning, diana.
Inequalities are cousins of Equations. They are almost the same, or they solve almost the same, except that in Inequalities, you need to change the sense or reverse the direction of the inequality sign when you multiply or divide both sides of the inequality by a negative number or negative value.
8 +b < -3
To sove for b, isolate it.
There is an 8 with b on the lefthand side of the inequality. To leave b alone on that side, remove or move or tranpose the 8 to the other side. The shortcut is to move the 8 and make it (-8) to the other side. The longcut [] is subtract 8 from both sides, thus,
b < -3 -8
b < -11 ---------------answer.
--------------------------------------------
h/4 > 16
There is a denominator 4 with h on the lefthand side. Or h is being divided by 4 at the lefthand side. To isolate h, eliminate that denominator 4 by multiplying both sides of the inequality by 4, thus,
h > 16*4
h > 64 --------------answer.
---------------------------------------------------
-7z < 21
There is (-7) attached or multiplied to z at the lefthand side. To isolate z, eliminate that barnacle (-7) by dividing both sides of the inequality by (-7).
Aha! We are dividing both sides by a negative number. So change the sense of the inequality. The "<" now will become ">" when we divide by (-7), thus,
z > 21/(-7)
z > -3 -----------------------answer.