1. Equations & Inequalities

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

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.

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

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)

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

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

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^2/3 = 16

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^3/2 = 27

Solve and check each linear equation. 4x + 9 = 33

Solve and check each linear equation. 2x - 7 = 6 + x

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/3 = x/2 - 2

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 4/x = 5/2x + 3