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
\(2x\geq-6\) ----> inequality A
Divide by \(2\) both sides
\(x\geq-3\) ------> the solution inequality A is the interval [-3,∞)
\(x-1 < 0\) -----> inequality B
Adds \(1\) both sides
\(x < 1\) ------> 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
\(-7x<14\) ----> inequality A
Divide by \(7\) both sides
\(-x<2\) -----> multiply by \(-1\)
\(x>-2\)------> the solution inequality A is the interval (-2,∞)
\(3x+2\leq 8\) -----> inequality B
Adds \(-2\) both sides
\(3x\leq 6\)
Divide by \(3\) both sides
\(x\leq 2\) ------> 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
\(--8 ----> inequality A
rewrite
\(x-5>-8\)
Adds \(5\) both sides
\(x>-3\) ------> the solution inequality A is the interval (-3,∞)
\(x-5<-3\) -----> inequality B
Adds \(5\) both sides
\(x<2\) ------> 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
\(1\leq4x+1\) ----> inequality A
rewrite
\(4x+1\geq 1\)
Adds \(-1\) both sides
\(4x\geq 0\)
Divide by \(4\) both sides
\(x\geq 0\) ------> the solution inequality A is the interval [0,∞)
\(4x+1\leq 17\) -----> inequality B
Adds \(-1\) both sides
\(4x\leq 16\)
Divide by \(4\) both sides
\(x\leq 4\) ------> 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
\(1\leq -2x+7\) ----> inequality A
rewrite
\(-2x+7\geq 1\)
Adds \(-7\) both sides
\(-2x\geq -6\)
Divide by \(2\) both sides
\(-x\geq -3\) ------> multiply by \(-1\)
\(x\leq 3\) ------> the solution inequality A is the interval (-∞,3]
\(-2x+7<9\) -----> inequality B
Adds \(-7\) both sides
\(-2x<2\)
Divide by \(2\) both sides
\(-x<1\) ------> multiply by \(-1\)
\(x>-1\) ------> 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
\(3x-1<-7\) ----> inequality A
Adds \(1\) both sides
\(3x<-6\)
Divide by \(3\) both sides
\(x<-2\) ------> the solution inequality A is the interval (-∞,-2)
\(4x+9\geq 13\) -----> inequality B
Adds \(-9\) both sides
\(4x \geq 4\)
Divide by \(1\) both sides
\(x \geq 1\) ------> 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
\(-5x>15\) ----> inequality A
Divide by \(5\) both sides
\(-x>3\)
multiply by \(-1\)
\(x<-3\) ------> the solution inequality A is the interval (-∞,-3)
\(x-5>-6\) -----> inequality B
Adds \(5\) both sides
\(x>-1\) ------> 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
\(4-15x\geq 4\) ----> inequality A
Adds \(-4\) both sides
\(-15x\geq 0\)
Divide by \(15\) both sides
\(-x\geq 0\) -----> multiply by \(-1\)
\(x\leq 0\) ------> the solution inequality A is the interval (-∞,0]
\(12x>36\) -----> inequality B
Divide by \(12\) both sides
\(x>3\) ------> 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
