Use the addition property and/or the multiplication properties to find a and b.
If -4<x<5 then a<4x+5<b .
-4 < x < 5
-16 < 4x < 20
-11 < 4x+5 < 25
so, ...
-4 (4) < 4x < 5(4)
-16 < 4x < 20
-16 + 5 < 4x+5 < 20 + 5
-11 < 4x+5 < 25
XD WTF?
To find the values of a and b, we will use the given inequality -4 < x < 5, along with the expression 4x + 5.
First, we will determine the lower bound for a.
-4 < x implies -4 < 4x + 5 (Adding 5 to both sides)
-9 < 4x (Subtracting 5 from both sides)
Since we want to find a, we choose the smallest possible value for 4x, which occurs when x = -4, making 4x = -16. So, a must be less than -16.
Next, we will determine the upper bound for b.
x < 5 implies 4x + 5 < 4(5) + 5 (Multiplying both sides by 4)
4x + 5 < 20 + 5
4x + 5 < 25
Since we want to find b, we choose the largest possible value for 4x, which occurs when x = 5, making 4x = 20. So, b must be greater than 20.
Therefore, the solution is a < -16 < 4x + 5 < 25 < b.