Answers Mathematics II PretestQuestion 5

5

lesson pretestMultiple Choice

Pretest

Question 5 • Mathematics II

Consider the following sets. cap u is equal to x divides x is a real number cap A is equal to x divides x is a solutions to the inequality 3 x plus 4 is greater than or equal to 13 cap b is equal to x divides x is a solutions to the inequality 1 half x plus 3 is less than or equal to 4 What is the intersection of cap A and cap b ?

Answer

A

cap u

B

start set x such that 2 is less than x comma x is less than 3 end set

C

phi

D

start set x such that x is less than or equal to 2 or x comma 2 or x is greater than or equal to 3 end set

Explanation

For set A, solve 3x + 4 ≥ 13: subtract 4 and divide by 3 to get x ≥ 3. For set B, solve ½x + 3 ≤ 4: subtract 3 and multiply by 2 to get x ≤ 2. No real number can be both at least 3 and at most 2, so the intersection is empty, or φ.

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