1. Equations & Inequalities

Find all values of x satisfying the given conditions. y₁ = 2x² + 5x - 4, y₂ = - x² + 15x - 10, and y₁ - y₂ = 0

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Solve each equation in Exercises 41–60 by making an appropriate substitution. ${(y-\frac{8}{y})}^2+5(y-\frac{8}{y})-14=0$

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)² - 4(x - 5) - 21 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. $x^{\frac{2}{5}}+x^{\frac{1}{5}}-6=0$

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. $(x^2-x-4{)}^{\frac{3}{4}}-2=6$

Solve each equation in Exercises 41–60 by making an appropriate substitution. x^(-2) - x^(-1) - 6 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0

Solve each equation in Exercises 96–102 by the method of your choice. 2√(x-1) = x

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $\sqrt{2x + 19} - 8 = x$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 3) = x - 3

Solve each radical equation in Exercises 88–89. √ (2x-3) + x = 3

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.) | x² + 5x + 5 | = 1

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.) | x² - 9 | = x + 3