Select the postulate of equality or inequality that is illustrated. 3 + 2 5 and 3 + 2 = 5 are not both true. addition postulate of inequality the multiplication postulate of inequality the symmetric postulate of equality the transitive postulate of equality comparison postulate the reflexive postulate of equality the transitive postulate of inequality

comparison postulate.

Explanation.

The given inequality might be either 3 + 2 > 5 or 2 + 2 < 5. The reasoning and the result is the same for effects of this question.

The comparison postulate states that one and only one of the following statements is true: a = b, a > b, a < b.

This is, a is either equal, or greater than or less than b, but not equal and greater, or equal and less, or greater and less. One and only one of them is true.

So, since  3 + 2 = 5, the comparison postulate assures that the inequality cannot both be true. This is 3 + 2 is equal to 5, and not greater or less than 5.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4