What is the solution for 9 > x - 7?
x < 2
x > 2
x < 16
x > 16

Solve for x by simplifying both sides of the inequality, then isolating the variable.

x < 16

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instead of showing that the conclusion to be proved is true, you show that all of the alternatives are false. To do this, you must assume the negation of the statement to be proved. Then, deductive reasoning will lead to a contradiction: two statements that cannot both be true.