Exam 2: Equations and Inequalities

Solve the rational inequality. Write the solution set in interval notation. -A rectangular enclosure must have an area of at least $800 \mathrm { yd } ^ { 2 }$ . If 180 yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Solve the equation. - $- 6 [ - 5 x + 3 - 6 ( x + 1 ) ] = 2 x - 5$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 5 x - 1 ) ^ { 2 } = 9 ( 5 x - 1 ) - 18$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 12 } \cdot \sqrt { - 4 } } { \sqrt { 3 } }$

Solve the equation by the zero-factor property. - $2 x ^ { 2 } = - 27 x - 81$

Solve the problem. -Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total Interest for that year was $140, how much did Kevin invest in the mutual fund?

Solve the rational inequality. Write the solution set in interval notation. - $8 \geq \frac { 1 } { x }$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $16 x ^ { 2 } + 8 x + 1 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. -One maid can clean the house in 8 hours. Another maid can do the job in 6 hours. How long will it take them to do the job working together?

Write the statement as an absolute value inequality. -The number of non-text books read by college students ranges from 8 to 46 . Using $B$ as the variable, write an absolute value inequality that corresponds to this range.

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x + 3 } = \sqrt [ 4 ] { 10 x }$

Find the sum or difference. Write the answer in standard form. - $6 i + ( - 5 - i )$

Solve and graph the inequality. Give answer in interval notation. - $\frac { 9 x - 7 } { 8 } < \frac { 79 } { 9 }$

Solve the equation by completing the square. - $x ^ { 2 } + 3 x - 9 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\left( x ^ { 2 } - 3 \right) ^ { 1 / 2 } - ( x + 3 ) ^ { 1 / 2 } = 0$

Solve for the indicated variable. - $\frac { 1 } { A } = \frac { 1 } { m } + \frac { 1 } { t }$ , for $t$

Solve the problem. -A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 2 feet longer than the length of a shelf. If 22 feet of lumber is available for the entire unit (including the Shelves, but NOT the back of the bookcase), find the length and height of the unit.

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 90 liters of a 50% solution to get a 40% solution?

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 4$

Decide what values of the variable cannot possibly be solutions for the equation. - $x ^ { 1 / 2 } = 2 x ^ { 1 / 4 }$