1. Equations & Inequalities

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation.20 - x/3 = x/2

In Exercises 25-38, solve each equation.3x/5 = 2x/3 +1

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state.4/(x²+3x−10) + 1/(x²+9x+20) = 2/(x²+2x−8)

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation.3x/5 - x = x/10 - 5/2

Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. -6(2x+1) - 3(x-4) = -15x+1

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. I=Prt,for P (simple interest)

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.7/2x - 5/3x = 22/3

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. z = x-μ/σ, for x (standardized value)

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.2/(x - 2) = x/(x - 2) - 2

Solve each equation for x. 3x=(2x-1)(m+4)

In Exercises 61–66, find all values of x satisfying the given conditions.y1 = 5/(x + 4), y2 = 3/(x + 3), y3 = (12x + 19)/(x^2 + 7x + 12). and y1 + y2 = y3.

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation.5x + 9 = 9(x + 1) - 4x

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

Evaluate x^2 - (xy - y) for x satisfying 3(x + 3)/5 = 2x + 6 and y satisfying - 2y - 10 = 5y + 18.

Solve: x/(x−3)=2x/(x−3)−5/3