Inequalities I

Sol A Subtracting and 9 from both sides gives , and then multiplying by gives or . Therefore is the solution.

Sol B Multiplying both sides out gives , and then subtracting from both sides gives . Therefore , so the solution is given by .

Sol C Solving gives or , and solving gives or . Taking the values of satisfying both inequalities gives , so is the solution.

Sol D Solving gives or , and solving gives or . Taking the values of satisfying both inequalities gives , so is the solution.

Sol 1 iff iff iff , so the solution is .

Sol 2 iff iff iff iff , so the solution is .

Sol 3 iff iff iff , so is the solution.

Sol 4 iff iff iff or , so the solution is .

Sol 5 iff iff iff and iff , so the solution is .

Sol 6 can be broken up into the following two cases: a) If , then gives or ; so .

b) If , then gives or ; so .

Combining the solutions for the two cases gives that is the solution.

Sol 7 iff iff iff iff iff

or iff or iff or , so is the solution.