Answer:
Part 1)
Part 2) ![d > -80](https://tex.z-dn.net/?f=d%20%3E%20-80)
Part 3) ![r < -1](https://tex.z-dn.net/?f=r%20%3C%20-1)
Part 4) ![z>5](https://tex.z-dn.net/?f=z%3E5)
Part 5) ![i\geq 20](https://tex.z-dn.net/?f=i%5Cgeq%2020)
Step-by-step explanation:
<u><em>The question is</em></u>
Solve each inequality for the indicated variable
Part 1) we have
![2u+12](https://tex.z-dn.net/?f=2u%2B12%3C23)
subtract 12 both sides
![2u< 23-12\\2u](https://tex.z-dn.net/?f=2u%3C%2023-12%5C%5C2u%3C11)
Divide by 2 both sides
![u< 5.5](https://tex.z-dn.net/?f=u%3C%205.5)
The solution is the interval (-∞,5.5)
In a number line the solution is the shaded area at left of u=5.5 (open circle)
The number 5.5 is not included in the solution
Part 2) we have
![0.1d+8 >0](https://tex.z-dn.net/?f=0.1d%2B8%20%3E0)
subtract 8 both sides
![0.1d > -8](https://tex.z-dn.net/?f=0.1d%20%3E%20-8)
Divide by 0.1 both sides
![d > -80](https://tex.z-dn.net/?f=d%20%3E%20-80)
The solution is the interval (-80,∞)
In a number line the solution is the shaded area at right of d=-80 (open circle)
The number -80 is not included in the solution
Part 3) we have
![3-4r> 7](https://tex.z-dn.net/?f=3-4r%3E%207)
Subtract 3 both sides
![-4r>7-3\\-4r>4](https://tex.z-dn.net/?f=-4r%3E7-3%5C%5C-4r%3E4)
Divide by -4 both sides
Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol
![r < -1](https://tex.z-dn.net/?f=r%20%3C%20-1)
The solution is the interval (-∞,-1)
In a number line the solution is the shaded area at left of r=-1.1 (open circle)
The number -1.1 is not included in the solution
Part 4) we have
![13< 2z+3](https://tex.z-dn.net/?f=13%3C%202z%2B3)
Subtract 3 both sides
![13-3](https://tex.z-dn.net/?f=13-3%3C2z%5C%5C10%20%3C2z)
Divide by 2 both sides
![5](https://tex.z-dn.net/?f=5%3Cz)
Rewrite
![z>5](https://tex.z-dn.net/?f=z%3E5)
The solution is the interval (5,∞)
In a number line the solution is the shaded area at right of z=5 (open circle)
The number 5 is not included in the solution
Part 5) we have
![6\geq 9-0.15i](https://tex.z-dn.net/?f=6%5Cgeq%209-0.15i)
Subtract 9 both sides
![6-9\geq -0.15i\\-3\geq -0.15i](https://tex.z-dn.net/?f=6-9%5Cgeq%20-0.15i%5C%5C-3%5Cgeq%20-0.15i)
Divide by -0.15 both sides
Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol
![20\leq i](https://tex.z-dn.net/?f=20%5Cleq%20i)
Rewrite
![i\geq 20](https://tex.z-dn.net/?f=i%5Cgeq%2020)
The solution is the interval [20,∞)
In a number line the solution is the shaded area at right of i=20 (closed circle)
The number 20 is included in the solution