1. Equations & Inequalities

In Exercises 1–26, solve and check each linear equation. 3(x - 1) = 21

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (7x−4)/5x = 9/5 − 4/x

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 3(2x-5)-2(4x+1)=-5(x+3)-2

In Exercises 1–26, solve and check each linear equation. x - 5(x + 3) = 13

Solve each equation. 5/6x - 2x+ 4/3=5/3

In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x

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

In Exercises 1–26, solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)

Solve each equation. -4(2x-6) +8x= 5x+24+x

In Exercises 1–26, solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) - 3y + 3]

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x/3 = 6 - x/4

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).

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. 2/x + 1/2 = 3/4

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

In Exercises 99–106, solve each equation. - 2{7 - [4 -2(1 - x) + 3]} = 10 - [4x - 2(x - 3)]

Solve: 3x-1/5 + x+2/2 = -3/10. (Section 1.4, Example 4)

Find b such that (4x - b)/(x - 5) = 3 has a solution set given by {Ø}.