1. Equations & Inequalities

Solve and check each linear equation. 11x - (6x - 5) = 40

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4

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

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

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)

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