Solving systems of inequalities part 2
Lets review the distributive property
3(x – 4) = 3x – 3(4)= 3x – 12
-4 (2 – x) = -4 (2) - -4x = -8 + 4x
Sometimes you may see the distributive property in an inequality
Ex 1. 3(x -4) > 3 distribute first ( distributive property is alone on the left)
3x -12 > 3
inverse operations
+12 +12
3x
> 15 divide
3
3
X
> 5
This means that any number greater than 5 will be a solution. To check lets try 7.
Is 3(7 – 4) > 3? 3(3) > 3? Yes, 9 > 3!
Ex 2.
-2(x + 5) + 3 < -5
inverse operations to get the dist. Prop. alone.
-3 -3
-2(x + 5)
-2x – 10
+10
< -8
Now use dist. Prop.
< -8
+10
-2x < 2
-2 -2
X > -1
* Note: you must switch the sign since dividing by a neg.