what do you call a female bug that floats

Answer:
Part 1) T
Part 2) L
Part 3) A
Part 4) Y
Part 5) T
Part 6) I
Part 7) U
Part 8) A
Part 9) N
Part 10) G
Part 11) B
Part 12) A
Part 13) N
Part 14) R
Part 15) O
The final answer is
A buoyant girl ant
Step-by-step explanation:
see the attached figure to better understand the problem
Part 1) we have
[tex]2x\geq-6[/tex] ----> inequality A
Divide by [tex]2[/tex] both sides
[tex]x\geq-3[/tex] ------> the solution inequality A is the interval [-3,∞)
[tex]x-1 < 0[/tex] -----> inequality B
Adds [tex]1[/tex] both sides
[tex]x < 1[/tex] ------> the solution inequality B is the interval (-∞,1)
The solution of the system of inequalities is the interval -----> [-3,1)
The solution is the letter T
Part 2) we have
[tex]-7x<14[/tex] ----> inequality A
Divide by [tex]7[/tex] both sides
[tex]-x<2[/tex] -----> multiply by [tex]-1[/tex]
[tex]x>-2[/tex]------> the solution inequality A is the interval (-2,∞)
[tex]3x+2\leq 8[/tex] -----> inequality B
Adds [tex]-2[/tex] both sides
[tex]3x\leq 6[/tex]
Divide by [tex]3[/tex] both sides
[tex]x\leq 2[/tex] ------> the solution inequality B is the interval (-∞,2]
The solution of the system of inequalities is the interval -----> (-2,2]
The solution is the letter L
Part 3) we have
[tex]--8<x-5[/tex] ----> inequality A
rewrite
[tex]x-5>-8[/tex]
Adds [tex]5[/tex] both sides
[tex]x>-3[/tex] ------> the solution inequality A is the interval (-3,∞)
[tex]x-5<-3[/tex] -----> inequality B
Adds [tex]5[/tex] both sides
[tex]x<2[/tex] ------> the solution inequality B is the interval (-∞,2)
The solution of the system of inequalities is the interval -----> (-3,2)
The solution is the letter A
Part 4) we have
[tex]1\leq4x+1[/tex] ----> inequality A
rewrite
[tex]4x+1\geq 1[/tex]
Adds [tex]-1[/tex] both sides
[tex]4x\geq 0[/tex]
Divide by [tex]4[/tex] both sides
[tex]x\geq 0[/tex] ------> the solution inequality A is the interval [0,∞)
[tex]4x+1\leq 17[/tex] -----> inequality B
Adds [tex]-1[/tex] both sides
[tex]4x\leq 16[/tex]
Divide by [tex]4[/tex] both sides
[tex]x\leq 4[/tex] ------> the solution inequality B is the interval (-∞,4]
The solution of the system of inequalities is the interval -----> [0,4]
The solution is the letter Y
Part 5) we have
[tex]1\leq -2x+7[/tex] ----> inequality A
rewrite
[tex]-2x+7\geq 1[/tex]
Adds [tex]-7[/tex] both sides
[tex]-2x\geq -6[/tex]
Divide by [tex]2[/tex] both sides
[tex]-x\geq -3[/tex] ------> multiply by [tex]-1[/tex]
[tex]x\leq 3[/tex] ------> the solution inequality A is the interval (-∞,3]
[tex]-2x+7<9[/tex] -----> inequality B
Adds [tex]-7[/tex] both sides
[tex]-2x<2[/tex]
Divide by [tex]2[/tex] both sides
[tex]-x<1[/tex] ------> multiply by [tex]-1[/tex]
[tex]x>-1[/tex] ------> the solution inequality B is the interval (-1,∞)
The solution of the system of inequalities is the interval ----->(-1,3]
The solution is the letter T
Part 6) we have
[tex]3x-1<-7[/tex] ----> inequality A
Adds [tex]1[/tex] both sides
[tex]3x<-6[/tex]
Divide by [tex]3[/tex] both sides
[tex]x<-2[/tex] ------> the solution inequality A is the interval (-∞,-2)
[tex]4x+9\geq 13[/tex] -----> inequality B
Adds [tex]-9[/tex] both sides
[tex]4x \geq 4[/tex]
Divide by [tex]1[/tex] both sides
[tex]x \geq 1[/tex] ------> the solution inequality B is the interval [1,∞)
The solution of the system of inequalities is the interval ----->(-∞,-2) U [1,∞)
The solution is the letter I
Part 7) we have
[tex]-5x>15[/tex] ----> inequality A
Divide by [tex]5[/tex] both sides
[tex]-x>3[/tex]
multiply by [tex]-1[/tex]
[tex]x<-3[/tex] ------> the solution inequality A is the interval (-∞,-3)
[tex]x-5>-6[/tex] -----> inequality B
Adds [tex]5[/tex] both sides
[tex]x>-1[/tex] ------> the solution inequality B is the interval (-1,∞)
The solution of the system of inequalities is the interval ----->(-∞,-3) U (-1,∞)
The solution is the letter U
Part 8) we have
[tex]4-15x\geq 4[/tex] ----> inequality A
Adds [tex]-4[/tex] both sides
[tex]-15x\geq 0[/tex]
Divide by [tex]15[/tex] both sides
[tex]-x\geq 0[/tex] -----> multiply by [tex]-1[/tex]
[tex]x\leq 0[/tex] ------> the solution inequality A is the interval (-∞,0]
[tex]12x>36[/tex] -----> inequality B
Divide by [tex]12[/tex] both sides
[tex]x>3[/tex] ------> the solution inequality B is the interval (3,∞)
The solution of the system of inequalities is the interval ----->(-∞,0] U (3,∞)
The solution is the letter A
see the complete answer in the attached file