1. Equations & Inequalities

In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x

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/(x² + 3x - 10) - 1/(x² + x - 6) = 3/(x² - x - 12)

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

In Exercises 45–46, describe in words the variation shown by the given equation. z = kx^2 √y

Solve each equation. $\(\left\)| \(\frac{2x + 3}{3x - 4}\) \(\right\)| = 1$

Solve the equation. $\(\frac{-5}{x+4}\)-3=\(\frac{x-1}{x+4}\)$

Force of Wind The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind of 40 mph exerts a force of 50 lb on a surface of 1/2 ft², how much force will a wind of 80 mph place on a surface of 2 ft²?

Find all values of x satisfying the given conditions. y₁ = 5(2x - 8) - 2, y₂ = 5(x - 3) + 3, and y₁ = y₂.

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

Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2(x-4)+3(x+5)=2x-2

Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7x + 13 = 2(2x-5) + 3x + 23

Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.

In Exercises 1–26, solve and check each linear equation. 2 - (7x + 5) = 13 - 3x

Solve and check each linear equation. 2x - 7 = 6 + x

Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. 5/(2x) - 2/x = 6