Respuesta :

You call a female bug that floats a buoyant girl ant.

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

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