1. Equations & Inequalities

Find all values of x satisfying the given conditions. y₁ = (2x - 1)/(x² + 2x - 8), y₂ = 2/(x + 4), y₃ = 1/(x - 2), and y₁ + y₂ = y₃.

In Exercises 67–70, find all values of x such that y = 0.

y = 2[3x - (4x - 6)] - 5(x - 6)

In Exercises 67–70, find all values of x such that y = 0. $y = \frac{x + 6}{3x - 12} - \frac{5}{x - 4} - \frac{2}{3}$

Find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x

Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8

Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x/(x + 3) - 12/(x - 3) = (4x² + 36)/(x² - 9)

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x² + 3x - 10) - 1/(x² + x - 6) = 3/(x² - x - 12)

Evaluate x² - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).

In Exercises 99–106, solve each equation. [(3 + 6)² ÷ 3] × 4 = - 54 x

Solve each equation. 5 - 12x = 8 - 7x - [6 ÷ 3(2 + 5³) + 5x]

In Exercises 99–106, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)

Solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)