1. Equations & Inequalities

What is an identity equation? Give an example.

Solve each equation for x. 2(x-a) +b =3x+a

Including a 10.5% hotel tax, your room in San Diego cost \$216.58 per night. Find the nightly cost before the tax was added.

Solve each equation for x. x/(a-1) = ax+3

Solve each problem. See Examples 5 and 6. Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot (μg/ft³), eye irritation can occur. One square foot of new plywood could emit 140 μg per hr. (Data from A. Hines, Indoor Air Quality & Control.) A room has 100 ft² of new plywood flooring. Find a linear equation F that computes the amount of formaldehyde, in micrograms, emitted in x hours.

Solve each equation for x. a²x + 3x =2a²

Solve: $6\mid 1\text{–}2x\mid \text{—}7=11$.

Solve each equation. 3x+5 - 5(x+1)= 6x+7

Solve each equation. 5x-2(x+4)=3(2x+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. 5/2x - 8/9 = 1/18 - 1/3x

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

In Exercises 91–100, find all values of x satisfying the given conditions. y = |2 - 3x| and y = 13

In Exercises 137–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation |x| = - 6 is equivalent to x = 6 or x = - 6.

Solve each equation. 6(3x-1)= 8 - (10x-14)

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