1. Equations & Inequalities

Write each formula as an English phrase using the word varies or proportional. r = d/t, where r is the speed when traveling d miles in t hours.

Solve each equation. x/x+2 + 1/x+3 = 2/(x²+2x)

What happens to y if y varies directly as x, and x is halved?

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x + 7 = 7(x + 1) - 3x

Period of a Pendulum The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. Find the period when the length is 121 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 6π seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x

Solve: x/(x−3)=2x/(x−3)−5/3

In Exercises 1–26, solve and check each linear equation. 16 = 3(x - 1) - (x - 7)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 1/R = 1/R₁ + 1/R₂ for R₁

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

Solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as the second power of x. (y=kx²)

Solve each equation for the specified variable. (Assume all denominators are nonzero.) 1/R=1/r_1 + 1/r_2, for R

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