Why do you switch the inequality sign when multiplying or dividing by a negative?

Is δ pmr similar to δ smn ? if so, which postulate or theorem proves these two triangles are similar?

What is 32+4 x (16 x 1/2) -2 show your work}

Let the closed interval [a , b] be the domain of function f. the domain of f(x - 3) is given by (a) the open interval (a , b) (b) the closed interval [a , b] (c) the closed interval [a - 3 , b - 3] (d) the closed interval [a + 3 , b + 3]