Solve each equation in Exercises 83–108 by the method of your choice. $2x^2-7x=0$

Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4

Exercises 177–179 will help you prepare for the material covered in the next section. If $-8$ is substituted for x in the equation $5x^{\frac{2}{3}}+11x^{\frac{1}{3}}+2=0$, is the resulting statement true or false?

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $5x^4-20x^2=0$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $4x^3-12x^2=9x-27$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $4y^3-2=y-8y^2$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $3x^4=81x$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 3) = x - 3

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $\sqrt{2x + 19} - 8 = x$

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 8) - √(x - 4) = 2

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(2x + 3) + √(x - 2) = 2

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $\sqrt{1+4\sqrt{x}}=1+\sqrt{x}$

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^3/2 = 27

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^2/3 = 16

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. $(x^2-x-4{)}^{\frac{3}{4}}-2=6$

Solve each equation in Exercises 41–60 by making an appropriate substitution. $9x^4=25x^2-16$

Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. $x^{\frac{2}{5}}+x^{\frac{1}{5}}-6=0$

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)² - 4(x - 5) - 21 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. ${(y-\frac{8}{y})}^2+5(y-\frac{8}{y})-14=0$

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x| = 8

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x - 2| = 7

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| = 5

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|3x - 2| = 14

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 7|5x| + 2 = 16

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|4 - (5/2)x| + 6 = 18

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|