Exam 1: Equations, Inequalities, and Applications

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - $- 9 x - 21 \leq - 3 ( 2 x + 9 )$

Solve the linear inequality. Express the solution in set-builder notation. - $\frac { 5 } { 2 } x + 4 < \frac { 2 } { 5 }$

Find all solutions. - $x ^ { 3 } + 2 x ^ { 2 } + 9 x + 18 = 0$

Solve the equation after making an appropriate substitution. - $3 x ^ { - 2 } - 4 x ^ { - 1 } - 4 = 0$

Solve the polynomial inequality. Express the solution in interval notation. - $( x + 7 ) ( x + 4 ) ( x - 5 ) < 0$

Solve the problem. -An airplane flies 450 miles with the wind and 330 against the wind in the same length of time. If the speed of the wind is 20, what is the speed of the airplane in still air?

Solve the equation after making an appropriate substitution. - $x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } + 10 = 0$

Solve the radical equation. - $\sqrt [ 3 ] { 3 x + 2 } = - 5$

Solve the rational inequality. Express the solution in interval notation. - $\frac { x - 5 } { x + 7 } < 0$

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

Determine whether the equation is linear or nonlinear. - $\sqrt { 5 } x + 3 = 0$

Perform the indicated operations and write the result in standard form. - $\frac { - 36 + \sqrt { - 108 } } { 6 }$

Solve the equation. -0.50x - 0.20(20 + x)= 1.00(20)

Solve the problem. -A certain store has a fax machine available for use by its customers. The store charges $2.50 to send the first page and $0.70 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $10.20.

Solve the problem. -Janet is training for a triathlon. Yesterday she jogged for 12 miles and then cycled another 31.5 miles. Her speed while cycling was 6 miles per hour faster than while jogging. If the total time for jogging and cycling was 3.75 hours, at what rate did she cycle?

Solve the problem. -The manager of a coffee shop has one type of coffee that sells for $7 per pound and another type that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a mixture that will sell for $10 per pound. How many pounds of the $7 coffee should be used?

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - $- 7 \leq - 2 x + 3 < - 5$

Perform the desired operation. Write the answer in the form a + bi. - $4 \mathrm { i } ( 8 - 5 \mathrm { i } )$

Write the expression in the standard form a + bi. - $\frac { 4 + 5 i } { 5 - 4 i }$

Solve the inequality. Express your answer using interval notation. - $| x + 1 | - 5 \leq 1$