Exam 1: The Real Numbers

Write the union as a single interval.

Let . Find a number B such that A + B is rational.

Perform the indicated operation.

Simplify the given expression as much as possible. 7(m + 7n) + 6m

Write the set as an interval or as the union of two intervals.

Simplify the given expression as much as possible.

Find all numbers x satisfying the equation.

Find all numbers with absolute value 6.

Let . Find an irrational number B such that the product AB is rational

Perform the indicated operation.

Let . Find a number B such that A + B is irrational.

Which of the following alternatives corresponds to the interval (2, 9]?

Which of the following intersections corresponds to the interval [-1, 5)? I II III

Let and . Find a number C such that A + B + C equals 10.

The division of an irrational number and a non-zero rational number is irrational.

Expand the given expression. (x - 2y + 3z)²

Which of the following is true?

For which values of a does the expression Correspond to a rational number?

Find the smallest positive number b such that is rational.

Which of the following expressions equals 7x - y? I. 7(x - 2y) + 2(7 - 1)y + y II. 2y + 7(x - 1) + (7 - 3y) III. 2(7x - y) + (y - 7x)