Solve each inequality. Give the solution set using interval notation.

$-8>3x-5>-12$

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

$9x^2+11x+4=0$

Simplify each power of i. i²⁵

Simplify each power of i. i²⁹

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.

$\mid y\mid =-x$

Solve each equation. See Examples 8 and 9. (x-1)^2/3+(x-1)^1/3 -12 = 0

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

$8x^2-72=0$

Simplify each power of i. i²⁶

Solve each inequality. Give the solution set using interval notation. x²-3x ≥ 5

Solve each equation. See Examples 8 and 9. (2x-1)^2/3+2(2x-1)^1/3-3=0

Simplify each power of i. i²³

Simplify each power of i. i²⁷

Solve each equation. See Examples 8 and 9. (x+5)^2/3+(x+5)^1/3-20=0

Solve each equation. See Examples 8 and 9. 4(x+1)⁴-13(x+1)²=-9

Answer each question. Find the values of a, b, and c for which the quadratic equation. $a{x}^2+bx+c=0$ has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.)

$4,5$

Solve each inequality. Give the solution set using interval notation. 3x+6 / x-5 > 0

Answer each question. Find the values of a, b, and c for which the quadratic equation. $a{x}^2+bx+c=0$ has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.)

$-3,2$

Solve each inequality. Give the solution set using interval notation. x+7 / 2x+1 ≤1

Simplify each power of i. i^-13

Solve each inequality. Give the solution set using interval notation. 3x-2/x - 4 > 0

Solve each equation. See Examples 8 and 9. 6(x+2)⁴-11(x+2)²=-4

Solve each inequality. Give the solution set using interval notation. 5x+2/x +1 < 0

Solve each equation. See Examples 8 and 9. 8(x-4)⁴-10(x-4)²=-3

Simplify each power of i. 1/i^-11

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.)

Solve each inequality. Give the solution set using interval notation. 3/x-1 ≤ 5/x+3

Simplify each power of i. 1/i^-12