Answer:
Part 1) [tex]u< 5.5[/tex]
Part 2) [tex]d > -80[/tex]
Part 3) [tex]r < -1[/tex]
Part 4) [tex]z>5[/tex]
Part 5) [tex]i\geq 20[/tex]
Step-by-step explanation:
The question is
Solve each inequality for the indicated variable
Part 1) we have
[tex]2u+12<23[/tex]
subtract 12 both sides
[tex]2u< 23-12\\2u<11[/tex]
Divide by 2 both sides
[tex]u< 5.5[/tex]
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
[tex]0.1d+8 >0[/tex]
subtract 8 both sides
[tex]0.1d > -8[/tex]
Divide by 0.1 both sides
[tex]d > -80[/tex]
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
[tex]3-4r> 7[/tex]
Subtract 3 both sides
[tex]-4r>7-3\\-4r>4[/tex]
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
[tex]r < -1[/tex]
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
[tex]13< 2z+3[/tex]
Subtract 3 both sides
[tex]13-3<2z\\10 <2z[/tex]
Divide by 2 both sides
[tex]5<z[/tex]
Rewrite
[tex]z>5[/tex]
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
[tex]6\geq 9-0.15i[/tex]
Subtract 9 both sides
[tex]6-9\geq -0.15i\\-3\geq -0.15i[/tex]
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
[tex]20\leq i[/tex]
Rewrite
[tex]i\geq 20[/tex]
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
