1. Equations & Inequalities

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

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. 3/(2x - 2) + 1/2 = 2/(x - 1)

Find all values of x satisfying the given conditions. y₁ = 5(2x - 8) - 2, y₂ = 5(x - 3) + 3, and y₁ = y₂.

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

What is an identity equation? Give an example.

What is a conditional equation? Give an example.

What is an inconsistent equation? Give an example.

Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8

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)