BackThe 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).
Solve each problem. See Example 1. The perimeter of a triangular plot of land is 2400 ft.The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot.
Solve each problem. See Example 4. Zhu inherited \$200,000 from her grandmother. She first gave 30% to her favorite charity. She invested some of the rest at 1.5% and some at 4%, earning \$4350 interest per year. How much did she invest at each rate?
Solve each equation. | (x - 4)/ 2| = 5
Solve each equation. ∜(3x+1)=1
The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?
Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.)
A. 5x+3 =11
B.12x+6 =-4
C.100x =50(x+3)
D. 6(x+4) =x+24
Find all values of x satisfying the given conditions. y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.
Solve each problem. How long will it take a car to travel 400 mi at an average rate of 50 mph?
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 8) - √(x - 4) = 2
Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.