Solve each rational inequality. Give the solution set in interval notation. (x+2)/(2x+3)≤5

Solve each rational inequality. Give the solution set in interval notation. (2x-3)/(x²+1)≥0

Solve each equation. (2x+3)^2/3 + (2x+3)^1/3 - 6 = 0

Find each quotient. Write answers in standard form. 8 / -i

For each equation, solve for x in terms of y. 2x² + 4xy - 3y² = 2

For each equation, (b) solve for y in terms of x. See Example 8.

$2x^2+4xy-3y^2=2$

Solve each equation. See Example 7. (3x+7)^1/3-(4x+2)^1/3=0

Solve each rational inequality. Give the solution set in interval notation.

Solve each rational inequality. Give the solution set in interval notation. (5-3x)²/(2x-5)³>0

To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x² - x | = 6, work Exercises 83–86 in order. For x² - x to have an absolute value equal to 6, what are the two possible values that x may assume? (Hint: One is positive and the other is negative.)

Solve each equation. (2x-1)^2/3 = x^1/3

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.) x² - 8x + 16 = 0

Find each quotient. Write answers in standard form. 2 / 3i

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

$11x\ge 2(x-4)$

Solve each rational inequality. Give the solution set in interval notation. (5x-3)³/(25-8x)²≤0

Solve each equation. (x-3)^2/5=(4x)^1/5

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.) 3x² + 5x + 2 = 0

Solve each rational inequality. Give the solution set in interval notation. (2x-3)(3x+8)/(x-6)³≥0

Solve each equation. x^2/3 = 2x^1/3

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

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

$7x-2(x-3)\le 5(2-x)$

Solve each equation. 3x^3/4 = x^1/2

Solve each rational inequality. Give the solution set in interval notation. (9x-11)(2x+7)/(3x-8)³>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.) 4x² = -6x + 3

Solve each equation. 2x⁴-7x²+5=0

Solve each inequality. Give the solution set using interval notation. 5 ≤ 2x -3 ≤ 7

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.) | 3x² + x | = 14

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

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

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.) | 3x² - 14x | = 5

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.

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